Doesn't there need to be some kind of proof for you to get prosecuted for something?

Here in the states, 99.9% of the time a court will side with the policeman over you, unless he blatantly screwed something up. I have heard a policeman in court give testimony that he "judged" the vehicle to be traveling at X speed, VISUALLY, and it was accepted as fact.

It sucks, but that's the way it is.