Who dun it?

Question: It was a sunday. a man lived in a house with his wife, a butler, a maid, and a cook. He went out for breakfast, and when he came back his wife was dead. the butler said he was cleaning rooms. the maid said she was dusting and vacuuming. The cook said he was preparing lunch. The police could not find any evidence so they found 3 other suspects. The mailman, the neighbor, and the local barber. The barber said he was cutting hair. the neighbor said he was out for lunch. the mailman said he was delivering mail. The police then arrested the murderer. Who was the murderer and how did the police know who it was?