Lets play a game /sci/:

You are given a set 13 cards from a 52 card deck.
Another deck draws cards 1 by 1.

After 31 cards have been drawn, what are the chances that your set matches theirs?

Order is not important.
For simplicity, you do not need to work out the odds after any other number of draws, just "at 31 cards".

Show your workings.

Its not 1/635 billion.