The second question of the last scenario is exactly equivalent to “show me the ace you’ve chosen”, which gives zero new information about whether you have two aces or not.
The states of knowledge in scenarios 1 and 2 aren’t equivalent.
It’s true that the same possibilities are ruled out in scenario 2 that are ruled out in scenario 1 (and therefore, the same possibilities remain in both scenarios), but in scenario 2 the observation that one of the cards is the ace of spades does more than rule out possibilities, it also shifts the probability mass from the AS/AH possibility toward the AS/2C and AS/2D possibilities, in such a way that the probability attached to the AS/AH possibility doesn’t change.
Put more succinctly, the remaining possibilities are the same in both scenarios, but the probabilities attached to these possibilities are different, so it’s not true that the states of knowledge are the same.
Argument 2.
The second question of the last scenario is exactly equivalent to “show me the ace you’ve chosen”, which gives zero new information about whether you have two aces or not.
This is the clearest answer I’ve seen.
But Argument 1 has an intuition pump based on equivalent states of knowledge, too, and it’s wrong! ;)
This equivalence works but does not generalize well, as it would fail on a three As two 2s variant.
The states of knowledge in scenarios 1 and 2 aren’t equivalent.
It’s true that the same possibilities are ruled out in scenario 2 that are ruled out in scenario 1 (and therefore, the same possibilities remain in both scenarios), but in scenario 2 the observation that one of the cards is the ace of spades does more than rule out possibilities, it also shifts the probability mass from the AS/AH possibility toward the AS/2C and AS/2D possibilities, in such a way that the probability attached to the AS/AH possibility doesn’t change.
Put more succinctly, the remaining possibilities are the same in both scenarios, but the probabilities attached to these possibilities are different, so it’s not true that the states of knowledge are the same.