The positive three-digit integer $N$ has a ones digit of $0$. What is the probability that $N$ is divisible by $4$? Express your answer as a common fraction.
An integer is divisible by 4 if and only if a number formed from the last two digits is divisible by 4. If the units digit is 0, all the numbers with even tens digits are divisible by 4 (00, 20, 40, 60, 80), and all the numbers with odd tens digits are not (10, 30, 50, 70, 90). Since there are the same number of even digits as odd digits, there is a $\boxed{\frac{1}{2}}$ probability that $N$ is divisible by 4.