Why is returning a non-initialized value considered undefined behavior?

While reading this I saw a UB that I don't understand, hoping you can clarify

size_t f(int x)
{
    size_t a;
    if(x) // either x nonzero or UB
        a = 42;
    return a; 
}

I guess the UB is due to a not having an initialized value, but isn't that it's defined behavior? Meaning, f(0) will return the value held by variable a, whatever it is (I consider this to be something like rand()). Must we know what value the code snippet returns for the code to have a well-defined-behavior?