How to calculate the average case time complexity of an algorithm?

It's usually easy to calculate the time complexity for the best case and the worst case, but when it comes to the average case especially when there's a probability p given, I don't know where to start.

Let's look at the following algorithm to compute the product of a matrix:

int computeProduct(int[][] A, int m, int n) {
    int product = 1;
    for (int i = 0; i < m; i++ {
        for (int j = 0; j < n; j++) {
            if (A[i][j] == 0) return 0;
            product = product * A[i][j];
        }
    }
    return product;
}

Suppose p is the probability of A[i][j] being 0 (i.e. the algorithm terminates there, return 0); how do we derive the average case time complexity for this algorithm?