The product $ ab $ is prime only when either $ a $ or $ b $ is one. Since $ b $ cannot equal 1, $ a $ must equal 1, and this occurs with probability $ \frac14 $. Furthermore, $ b $ must be prime, so $ b $ must equal 5 or 7, and this occurs with probability $ \frac25 $. Therefore, the probability that $ ab $ is prime is $ \frac14\cdot \frac25 = \boxed{\frac1{10}} $.