# Probability of hash function to return a value in the expected range

How do I find out the probabillity for the following:

Let $$p$$ be a prime number. Let $$a$$ be a random number in $${ 1, … p-1 }$$ and b a random number in $${ 0, … p-1 }$$. Let $$k: mathbb{N} to {0, …, p-1}$$, defined as $$k(x) = ax + bmod p$$.

For a $$x neq 0$$ and $$i$$ a random number in $${ 1, … p-1 }$$, what is the probabillity:
$$Pr(k(x) = i)$$.