Empty Hands
Senior Master
Who cares? It depends on which conclave was valid. You just don't get a bunch of dudes in red hats together and go around electing popes. The idea itself is ridiculous!
Yet, that's exactly what happened. All 3 conclaves were valid IIRC. Indeed, that would be why the Council of Constance was called to resolve the dispute, and did so by making all 3 Popes step down. If only one Pope was clearly valid, then he would not have been asked to step down, yes?
I used "claimant" because it's more accurate to say than to say "three popes" like you did (which is not just false but self-contradictorarily so). It would have been better to say one pope and two claimant, I admit.
Well, that's part of the problem, because no one at the time knew which was the Pope and which were the claimants. Which is how we get into this logical conundrum if you insist that there is only one real Pope, which leads to all sorts of uncomfortable implications because there is no way to tell who it is. The "real" Pope was forced to step down like the rest.
Of course, this is only really a problem because Apostolic Succession is treated like a logic game or a computer program. If there were no Pope or 50 of them, I'm sure the Creator of the Universe would have no trouble assigning that power in a just and reasonable way over the long term. People tend to treat that Creator like a computer program though, which doesn't make much sense if you think of God as a thinking creature. Another reason why Pascal's Wager makes no sense.