(a/b) (mod P) = (a * b^-1) (mod P) = (a (mod P) * b^-1 (mod P)) (mod P).

Now, by Fermat's theorem, b-1 (mod P) will be b^P-2 (mod P). Of course, for this b and P must be co-prime to each other and P must be a prime. So, (a/b) (mod P) = (a (mod P) * b^P-2 (mod P)) (mod P). works only if P is prime and a,b are coprime to P