I would judge today that improved existing systems have a high probability of hitting and destroying an incoming supersonic target.
What have you done for the fleet today?
The Iraqis shoot at everything in the sky. So far they're one for last decade, on a drone using manned aircraft. Shootin' and hittin' are two different things. All successful air defense fire-control systems today are "closed loop", either the round has sensors that are fed to a navigation system to continuously reduce aiming errors, or the firing system continously corrects its aim on a moving target.
The WW-II era SCR-584 was something of an exception, it would track V1 "buzz bombs" and predict their position at the time that a radar fused AAA shell would arrive. -It was a predictor, rather than a closed loop system, sort of like a submarine torpedo. The V1 flew a straight, level and low course that made it an easy target. Alfred Price's book Instruments of Darkness contains an interesting example of a photo plate used by the Germans to track a V1. They couldn't understand why so many of them mysteriously disappeared after crossing the channel. Of course they used radar fused shells which the Germans didn't know about. The shell was fragmentation type, it would explode sending thousands of small projectiles into the path of the V1. It still took about five shells on average to bring down a V1.
It's relatively easy to track a target with a laser in clear weather. The hard part is generating very high power and focusing it on a moving target through an inhomogenous atmosphere. As a pure guess, it probably takes about 10 -100 kW applied for several seconds to "damage" an artillery shell. On the order of the amount of power delivered by a blowtorch. If it was easy, anyone could do it.