Sounds like you mean the exact same hand. So since there's no specific hand required the first time can be any two cards, and you really just need to see what the odds of them repeating 3 more times are.
So picture your next deal. You are getting a card out of 52 card and it needs to be one of the 2 previous cards. So you have a 2/52 chance of this happening. The next card dealt will represent a 1/51 chance. This repeats for the next two rounds. To get the cumulative odds, multiply each time. So:
(2/52)(1/51)(2/52)(1/51)(2/52)(1/51) = 1/2,331,473,976