Geometry

Question Analysis
This question involves conditional probability in the context of card - drawing without replacement.
The main focus is on adjusting the sample space and the number of favorable outcomes based on the first event.

Key Concept Explanation
Conditional probability in the case of sequential events without replacement requires us to consider how the first event affects the second event.
After the first non - ace card is drawn, the total number of cards and the number of aces in the remaining deck change.

Step-by-Step Solution
When the first card is not an ace, there are 48 non - ace cards initially.
After drawing one non - ace card, there are 51 cards left in the deck, and 4 of them are aces.
So the probability that the second card is an ace given that the first card was not an ace is

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