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:
$Pr(k(x) = i)$.