Sherlock-style situation puzzles

Sherlock Holmes was walking down the corridor. Suddenly he heard a woman screaming, “Please, John, don’t kill me!” A shot rang. Holmes burst into the room. In one corner lay a dead woman and a gun. In another corner stood a postman, a lawyer, and an accountant. Sherlock looked at them, approached the postman, and grabbed him: “I will arrest you for killing this woman.” It was really the postman who killed this woman, but how could Holmes know it?

A man is driving his car while listening to the radio when suddenly the radio goes silent. He then decides to leave the road and throw himself off the top of a cliff.