What is the probability that a card randomly drawn from a standard deck of 52 cards is not a king?

There's a deck of cards (52 cards total). When drawing two cards from the deck, what is the probability of both the cards not being kings?

So, here's my line of thought. The chance of NOT getting a king is $\frac{48}{52}$ (because there are 4 kings). Then, the chance of, when removing 2 cards, not getting any king, would be $\frac{48}{52} \times \frac{48}{52}$, because of this rule:

$$P(A\rm{\,and\,}B)=P(A\cap B)=P(A)P(B),$$

I got this exercise on a book and on the Answers, it says it's $\frac{47}{221}$. That's $\sim21%$, is there a chance the answers are wrong, because when I think of it, the probability should be much higher (like the one I got, $\sim85%$).

Notes: The first card is not replaced. There are 4 kings, the rest of the cards shouldn't really matter.