Tragedy in Three Acts - Agatha Christie

Thirteen guests arrived at the famous actor's house for a dinner party, but it was an ill-fated party for one of them; Mr. Babbington choked on his drink, and soon fell dead.

But when the sample of the drink left in the cup was sent to a lab for testing, no trace of the poison was found. The other thing that seemed confusing to the famous detective was that this crime seemed to have no motive to commit it!