Why a condition that contains a pointer always returns true?

For example consider the following code. The pointer p points to the variable a that contains a nonzero value. Meaning, the condition should be true. So, if the program returns 1, I have no problem with that.

#include <iostream>

int main()
{
    int *p, a = 1;

    p = &a;

    if(p)
    {
        return 1;
    }

    return 0;
}

But for the following program the result is same too. Though the pointer this time points to a variable that contains 0. So, the condition should be false, but it is not.

#include <iostream>

int main()
{
    int *p, a = 0;

    p = &a;

    if(p)
    {
        return 1;
    }

    return 0;
}

So, what I am missing? Why the condition is always returning true? I am assuming the pointer has nothing to do with the value that it points to. Rather it is evaluating the condition on the basis of something else and I want to know that particular reason.