Consider the quadratic function \( f(x) = ax^2 + bx + a \) having two irrational roots, with \( a \) and \( b \) being two positive integers, such that \( a, b \leq 9 \).
If all such permissible pairs \( (a, b) \) are equally likely, what is the probability that \( a + b \) is greater than 9?