Since you replace the card every time, the four experiments are exactly the same, repeated four times.
In each experiment, you have four kings in the deck (one for each suite), and 52 cards in total. This means that the probability of drawing a king with each pick is 4/52 = 1/13.
As we just discussed, the events are independent, since everytime you pick a card you reinsert it in the deck, thus "resetting" the experiment. Think it this way: there is no difference in picking and replacing four times form the same deck, or picking from four different decks. This means that the events are independent, and we want an event with probability 1/13 (drawing a king) to happen four times in a row.
In this kind of scenarios, you have to multiply the probabilities of each event, so the answer will be
