Compute P(third Ace | Ace in first two)

Three cards are drawn without replacement from an ordinary 52-card deck. If at least one of the first two cards is an Ace, what is the probability that the third card will be an Ace? State and justify any independence or symmetry reasoning you use. Then generalize: if a deck has $N$ cards and $A$ Aces, and the first $m$ cards ($m \ge 2$) contain at least one Ace, what is $P(\text{card } m+1 \text{ is an Ace})$?

Overview: This problem tests conditional probability, dependence versus independence, symmetry arguments, and combinatorial reasoning for sampling without replacement.