Take the current target and divide by 115792089237316195423570985008687907853269984665640564039457584007913129639935.

That number represents the probability of any given hash solving a block.

You now have a very standard binomial probability problem where n represents the number of hashes your hardware is capable of generating over the amount of time you're considering.

If you call the above calculated number P, then the probability of producing a hash that qualifies for the target difficulty after n hashes is going to be 1 - (1-P)^n