Masechet Bechorot, Perek Chet, Mishnah. The Mishnah here has more cases of questionable Bechorim (firstborns). The Mishnah says there are two wives of two different men, and neither wife had given birth before. The two wives gave birth to two boys, but we don't know which child is connected to which mother. Each of these men has to give five Sela'im (sela coins) to the Kohen (priest), even though neither man knows which child is his son. His wife definitely gave birth to a Bechor (firstborn), and therefore he is obligated in the mitzvah (commandment), and he has to give five Sela'im to the Kohen.
If one of the babies died within 30 days, but both fathers had already paid their five Sela'im, and they had both given the money to the same Kohen, then that Kohen has to return five Sela'im to the two fathers, even though we don't know which father is really entitled to the refund. One of the sons here didn't last the full 30 days, so one of them technically didn't have to give the money in Pidyon (redemption). But we don't know which one that was. What we do know with definite certainty is that the Kohen was not entitled to the 10 Sela'im. He's entitled to only five, and therefore he has to return the Sela'im to the fathers.
If both fathers come together with this claim and demand a refund, if only one father came to demand a refund, the Kohen could refuse, because he could say, “How do you know you're entitled to the money? How do you know you're the one whose son died? You don't know which son is yours.” So if they both come together, the Kohen has to return the five Sela'im to the fathers together, and they divide the money between them, however they see fit.
But if the fathers gave the money to two different Kohanim, each father giving his five Sela'im to a different Kohen, they don't have the ability to take the money back from the Kohanim. The money is in the possession of the Kohanim right now, and each Kohen could individually claim that he received the money for the living child, not for the one who passed away. The money is in the possession of the Kohen right now, and in order to extract it from him, to take it out of his possession, there has to be proof that he received the money for the Bechor that passed away. If they don't have the ability to give that proof because they don't know which son is really theirs, then the Kohen is not obligated to give them their money back.
Another case: Two women are married to two men, and each woman gave birth to her first child. But in this case, one woman gave birth to a male and the other one to a female—a girl—and the babies became mixed up. The fathers are exempt from giving the five Sela'im to the Kohen, because each father could say that his wife gave birth to the girl. There's no way to prove which one gave birth to the boy; each father can claim that his wife gave birth to the girl. One of them has a claim that his child was not the boy. But later on, when the boy grows up, he's required to do Pidyon HaBen (redemption of the firstborn) on himself, since he knows that he is definitely a Bechor.
If the two women gave birth to two females and one male, or they gave birth to two males and two females, but we don't know who gave birth to what and in what order, there's nothing here for the Kohen whatsoever. It's not certain even in this case that there is any Bechor. Maybe in the first case, the two nekevot were first. Maybe the two girls were born first from two different females, and then one of them had a zachar, one of them had a boy also. Or, in the case where there were two males and two females, both from two different sets of parents, maybe in this case the nekevot were both first, the girls were born first to each mother, and then they both had boys. So therefore, there's no case where we know with certainty that there even is a Bechor, and therefore the fathers are not obligated to pay any Pidyon HaBen.