Odds: Two 4 of a kinds in the same hand

Hi.

My brother and I were talking shortly after he won a hand in which his 4 of a kind beat someones full house. The board read 4 4 k k 5. My brother had a pair of 4's in the hole, his opponent had KQ.

After the hand I hypothetically asked him "would if a king came on the river?". He then asked "what would be the odds of that?" We then went tried pathetically to guess the odds with little to no knowledge about the math.

Anyways. My question is simply this: What are the odds of two people getting four of a kind in the same hand in a game of Texas Holdem? I tried using the search function but no luck. If you know a link that explains this that's fine or if you could give me those odds yourself I would greatly appreciate it.

Thanks in advance.