What is the probability that the second card is a king, given that the first card was a spade?

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I have the following questions. Part a- the answer is 4/51 as all the jacks are still in the pack. My question is why the answer to part b not the same as all the kings are still in the pack? Instead, the answer is 1/13, why?

A pair of cards are drawn from a standard pack of 52 cards. (a) What is the probability that the second card is a jack, given that the first card was an ace?

(b) What is the probability that the second card is a king, given instead that the first card was a spade?

In general, how should you approach these kind of questions? I find them difficult to visualise for harder problems..?

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Hint: For part (b), either the spade was the king of spades or it wasn't.