1. **State the problem:** We want to find the conditional probability that a card drawn is a spade, given that it is an ace. 2. **Recall the formula for conditional probability:** $$P(A|B) = \frac{P(A \cap B)}{P(B)}$$ where $A$ is the event "card is a spade" and $B$ is the event "card is an ace". 3. **Identify the events:** - Total cards in deck: 52 - Number of aces: 4 (one in each suit) - Number of spade aces: 1 4. **Calculate probabilities:** - $P(B) = \frac{4}{52}$ (probability card is an ace) - $P(A \cap B) = \frac{1}{52}$ (probability card is the ace of spades) 5. **Apply the formula:** $$P(A|B) = \frac{\frac{1}{52}}{\frac{4}{52}}$$ 6. **Simplify the fraction:** $$P(A|B) = \frac{1}{52} \times \frac{52}{4} = \frac{1}{4}$$ 7. **Interpretation:** Given that the card is an ace, the probability it is a spade is $\frac{1}{4}$. **Final answer:** $$\boxed{\frac{1}{4}}$$