Murder at the Vicarage

When Colonel Lucius Protheroe turns up dead at the vicarage, no one is surprised.  Even the local vicar says "killing him would be doing a service to the townsfolk".  While the vicar looks suspicious, two other people confess to the crime and Miss Marple is called in to solve the murder.  Miss Marple determines that the two people who confessed, Mrs. Protheroe and her lover Lawrence Redding, were indeed the murderers, and simply wanted to deflect guilt by admitting to the crime.  Miss Marple appears in later novels, The Body in the Library (1942) and 4:50 from Paddington (1957).

Murder at the Vicarage, published in 1930, courtesy 

http://www.agathachristie.com/stories/the-murder-at-the-vicarage.