police play the fundimental role legitimizing state power how this simple function assist in crime privention?

Answer 1

people who are going to commit crimes might not if they think they will get caught

Answer 2

Have to admit...not sure what your question is here, perhaps due to lack of punctuation. If I have a clue here, it is because if police enforce the laws that are in effect, they are legitimizing them and making them more enforceable when a criminal with a good lawyer tries to weasel around a law. If a law on the books has been enforced consistently by the police, it is setting a legal precedence that will be hard for a judge to overlook.