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I need help in how to frame this solution to this question.

There are $4$ Kings and $4$ Aces in the deck of 52 cards.

The probability of drawing a king is $= \frac{4}{52} = \frac{1}{13}$

The probability of drawing an Ace is $= \frac{4}{51}$

I'm not able to proceed beyond this.

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The probabilities you have written are for the case of sampling without replacement. The probability should be $\frac{1}{13}$ for both.

Since sampling is with replacement, the event of drawing a king and drawing an ace are independent. Therefore you can just simply multiply the two probabilities to get the answer.

Let A and B be events defined as A: King in the first draw, B: Ace in the second draw.

$P(A \cap B) = P(A) * P(B)$

$P(A \cap B) = \frac{4}{52} * \frac{4}{52} = \frac{1}{169}$

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