If there are 52 cards in a deck what is the probability of drawing two cards, and getting a king both times?

There are two cases here:

Case 1: First card chosen is a queen

452 ∗ 351 = 1221 452 ∗ 351 = 1221

Case 2: First card chosen is not a queen.

4852 ∗ 451 = 16221 4852 ∗ 451 = 16221

Adding both the cases, we get 17221 17221 = 452 452 = 113 113

In a simpler case: Think about it this way: Shuffle a deck of cards randomly. The probability of drawing a queen as your second card is the same as the probability that the second card in the deck is a queen, which is clearly 4/52.