What does "two randomly chosen integers" mean? You can't put a uniform distribution on the entire set of integers, so there is some interpretation involved.
Specifically, you seem to be using the following heuristic: Let $n$ be an random integer and $p$ be a prime. Then $Pr(p  n) = 1/p$.
This is perfectly sensible and number theorists use this kind of reasoning all the time. I was wondering, though, how you formulate this precisely,.
