Probability problem involving combinations

Here's the problem statement:

A deck of 52 cards contains 4 aces. If the cards are shuffled and distributed in a random manner to four players so that each player receives 13 cards, what is the probability that all 4 aces will be received by the same player?

The answer is $\displaystyle \frac{4 \binom{13}{4}}{\binom{52}{4}}$ but I'm really having trouble interpreting that answer and seeing how to get it. I understand that it's written as (# of favorable outcomes) / (total # of outcomes) but I would think that the total number of outcomes would be $\displaystyle \frac{52!}{(13!)^4}$, the number of ways to deal 52 cards to 4 people in groups of 13. I don't get where $\displaystyle \binom{52}{4}$ comes from. If anyone has any advice or a hint or something I'd love to hear it.