Question

What is the probability that the first card is a kingking and the second card is a kingking if the sampling is done with​ replacement?

Answer 1

You want to draw 2 kings from a 52 card deck. And you do it with replacement.
There are 4 kings in a standard deck. The probability of getting one of them is 
4/52 on the first draw.

For the second draw the probability is the same.
4/52

The probability for both happening is 
(4/52)*(4/52) = (1/13)*(1/13) = 1/169 = 0.001597