Jamaican police detained three of their own on Saturday after a video surfaced allegedly showing them beating and shooting a suspect to death.Police initially reported that the man stabbed a woman to death and then attacked the officers. They were said to have acted in self-defense.That story changed after the amateur footage, recorded by an unknown eyewitness, was broadcast on several television channels the following night.Police Chief Owen Ellington said Saturday the man was apparently unarmed and subdued when he was killed.Ellington praised whoever came forward with the video and said the department deeply regrets the incident.Jamaica has one of the highest rates of police killings in the Western Hemisphere, according to Amnesty International. It also has one of the world's highest murder rates.Thursday's killing took place in the town of Buckfield, about 20 miles (30 kilometers) from the resort city of Ocho Rios.