This problem has been a source of some controversy among probability theorists. Is the correct solution counterintuitive?

Remove all cards except aces and kings from a deck, so that only eight cards remain, of which four are aces and four are kings. From this abbreviated deck, deal two cards to a friend. If she looks at her cards and announces (truthfully) that her hand contains an ace, what is the probability that both her cards are aces? If she announces instead that one of her cards is the ace of spades, what is the probability then that both her cards are aces? Are these two probabilities the same?