Originally Posted by BruceZ
So we can just look at the overall probability that the last card in the deck is the 2c, and that's the probability that the card after the first ace will be the 2c. That is also true for the As.
Unless the first A you draw is the As. Then the probability the next card is the As is zero. This happens with a 1/4 probability. This is the part that is confusing to me. The rest of it all makes sense.
That is, if you changed the question so that it was "when I draw a K what is the probability the next card is either the 2c or the As?" it would obviously be the same. The part that tricks me is the fact that the As will be the card that gives you a probability of 0 for the As and (on average) a probability > 0 for the 2c when the As is draw first. This must be counteracted by the fact that the 2c can come up with a probability 0 when it is removed before an A occurs. The same cannot be said for the when the As occurs (i.e., it is never removed prior to an A coming) because it is already an A and requires that we stop.