Gemara

(R. Zeira): An Isur Kavu'a (it is from a place where all such matters are forbidden) is always considered an even doubt, whether this is a leniency or a stringency.

Question: What it his source for this law?

Answer #1 (Beraisa): If nine stores sell Kosher meat and one sells Neveilah and one bought from one of the stores and does not know from which, the meat is forbidden. If meat is found, we follow the majority.

Rejection: There we are stringent. (We cannot learn from there to be lenient.)

Answer #2 (Beraisa): If one frog is among nine Sheratzim and someone touched one of the 10 and does not know which, if this was in a Reshus ha'Yachid, he is Tamei. If it was in a Reshus ha'Rabim, he is Tahor.

Question: What is the source from the Torah?

Answer: D'Vei R. Yanai taught that Chachamim expound "He waits in hiding" to exempt one who throws a rock into a crowd (and killed someone).

Question: Who is in the crowd?

If there are nine Nochrim and one Yisrael, even if we follow the majority we cannot kill the murderer!

If half of them are Yisraelim, we are always lenient about a Safek in capital cases (we would not need a verse to teach the law)!

Answer: There are nine Yisraelim and one Nochri. Since they are Kevu'im, it is considered an even Safek.

Pesachim 9b: If there were nine piles of Matzah and one of Chametz, and a weasel took a piece from a pile, and we do not know from which it took, this is like the case of nine stores (it is considered an even Safek);

If a piece separated from one of the piles and a weasel took it, this is like the Seifa (if meat is found, we follow the majority).

Zevachim 71a (Mishnah): If any Korban became mixed with Chata'os ha'Mesos (which must be left to die), even if one was mixed with 10,000, all must die.

Question: Forbidden animals should be Batel amidst a majority of Heter!

73a - Answer (Rav Ashi): Living animals are important, so they are not Batel.

Question: We should force them to separate from each other. Each that separates is (assumed to be) from the majority!

Answer (Rava): Chachamim decreed not to do so, lest someone take in a way (i.e. from the mixture) that is considered Kavu'a.

Rishonim

Rif and Rosh (Chulin 33b and 8:20): If nine stores sell slaughtered meat and one sells Neveilah, and one bought from one of the stores and does not know from which, the meat is forbidden. If it was found in a Nochri's hand, it is permitted.

Rosh (ibid.): Every Isur Kavu'a is like an even Safek. Even though one piece of Isur is Batel in two pieces of Heter, that is when they are mixed and the Isur cannot be recognized. Bitul does not apply when the Isur is recognized in its place. Likewise, when an important matter became mixed and is not Batel, it is like an even Safek, like we find regarding animals (Zevachim 73a).

Question: When it is found in a Nochri's hand, why don't we decree lest one take from Kavu'a, like we decreed regarding animals?

Answer (Rosh): Here, the Isur is known in its place. People know that an Isur Kavu'a is like an even Safek and that one store sells Neveilah. Therefore, they will not buy meat before verifying that it is Kosher. If Isur was mixed and we permit to take from what separates, people might take from the mixture itself. R. Tam did not make this distinction. When a wolf entered a herd and made two or three animals Tereifah (we do not know which animals were scratched by the wolf's venomous claws), he permitted animals that separated. He must distinguish other Isurim from Kodshim and Avodah Zarah. This is unreasonable.

Rambam (Hilchos Ma'achalos Asuros 8:11): If nine stores sell slaughtered meat and one sells Neveilah, and one bought from a store and does not know from which, the meat is forbidden. Every Isur Kavu'a is like an even Safek. If meat is found in the market, we follow the majority. Anything that separated is assumed to be from the majority. If the majority of sellers are Yisraelim, it is permitted.

Magid Mishneh: The Rashba says that we forbid an Isur Kavu'a when it is by itself. If it became mixed with a majority of Heter and it is not recognized, it is permitted, because it is a Sefek-Sefeka (two doubts). He permits even a piece that is Re'uyah Lehiskaved (important enough to be served to honor a guest).

Hagahos Maimoniyos (5): The Rambam (16:10) holds like the Ri, who follows the majority to permit what separated from Kevi'us mid'Oraisa, even if we saw it separate. We decree only about Kevi'us mid'Rabanan, i.e. important things such as full creations that are never Batel mid'Rabanan. If we would permit something that separated from its Kevi'us, people would permit from the Kevi'us itself. R. Tam does not decree.

Teshuvas Rosh (20:17): When a piece separated from the mixture in front of us, the Safek started in a place of Kevi'us. We have no source to decree when a piece separated before there was a Safek, e.g. one bought meat and later we heard that there was a Tereifah in the market.

Poskim

Shulchan Aruch (YD 110:3): If nine stores sell slaughtered meat and one sells Neveilah and one bought from a store and does not know from which, the meat is forbidden. Every Isur Kavu'a is like an even Safek. Meat found in the market or in a Nochri's hand is permitted, for we follow the majority. Anything that separated is assumed to be from the majority.

Beis Yosef (DH u'Mah she'Chosav Kegon): The Rashba says that when an Isur is Kavu'a in its place, e.g. one does not know whether the sore in which he bought sells slaughtered or Neveilah meat, a piece is not Batel in the majority. This is even if it is not Re'uyah Lehiskaved. If the Isur was found in front of the stores, i.e. it was not taken from the place of Kevi'us, it is Batel even if it is Re'uyah Lehiskaved.

Shach (14): The Ro'oh says that if the Chazakah was that all 10 stores sell slaughtered meat, and after buying one heard that one of the stores sells Neveilah, the meat is forbidden. This is not like when meat separated, for the Safek is not due to (the meat) itself, rather, to the identity of the store. The Safek did not arise now. Rather, the Safek arose when he bought it, just we found out about it only now. The Rashba says that if one knows from which store he bought and later heard that a Tereifah animal was mixed with the Kosher ones in the market, even a Chatichah ha'Re'uyah Lehiskaved is permitted. The Safek is not about the store, only about whether the meat was from the Tereifah. Since he bought before he heard about the Tereifah, we say that the Safek came only later, so we follow the majority. However, the Ran (Chulin 33b DH Omar, citing Tosfos) says that an Isur is Kavu'a only if the Isur was known before he bought.

Rebuttal (Pri Chodosh 13): The Rashba holds like the Ran (even if he is unsure which store he bought from, it is permitted because the Safek arose only later).

Shach (14): The Tur holds like the Ran, and says that that the Rosh agrees. However, in Teshuvah 20:17 the Rosh permits when pieces were mixed and one bought before the Safek arose. It seems that he does not permit a Safek of stores.

Shach (16): If there was a Neveilah in one store and we do not know which store, even though this is an Isur Kavu'a, if meat separated not in front of us the Rosh forbids, lest one take from Kavu'a.

Shach (18): The Roke'ach says that if a child bought meat, it is as if a Nochri bought it.

Shulchan Aruch (ibid.): This is Torah law. Chachamim forbade it even if all the slaughterers and all the sellers are Yisraelim.

Rema: See Siman 63 (there are, the Rema permits in a case like this). We say that it came from the majority when we did not see it separate. If we did, or we saw the Nochri buy it, it is as if the Yisrael himself took it from there.

Source: Rashba (Toras ha'Bayis 4:2 30a) and Rosh (20:17), cited in Beis Yosef DH u'Mah she'Chosav d'Kiven), based on Pesachim 9b.