They Do It With Mirrors: Agatha Christie

Miss Marple senses clanger when she visits a friend living in Stoneygates, a rehabilitation centre for delinquents. Her fears are confirmed when someone shoots at the administrator. Though he is not injured, a mysterious visitor is less fortunate - shot dead simultaneously in another part of the building.
Pure coincidence? Miss Marple thinks not, and must use all her cunning to solve the riddle of the stranger`s visit... and his murder.