The probability of pulling any ball from a bag of n is 1/n. Doing it twice is 1/n *1/n = 1/n^2.
Since you're talking about 52!, I assume your question is actually "what is the probability of shuffling a deck twice and getting the same shuffle?". 1/(52!)^2 is approximately 1.5*10^-136.
For context there are about 10^68 atoms in the milky way, which is already an ungodly large number. imagine that every atom in the milky way contains an entire second milky way. If every atom in ALL those milky ways were assigned 2 random deck shuffles, only 33 of all those atom-atoms would be assigned the same deck twice (the math actually comes pretty close, it really surprised me).
The calculation to check that out end up being ( 10^68 )^2 / 52!^2 = 33