Death in the Clouds Christie Agatha

A woman is killed by a poisoned dart in the enclosed confines of a commercial passenger plane. Flying from Paris to London.

From seat No.9, Hercule Poirot was ideally placed to observe his fellow air passengers. Over to his right sat a pretty young woman, clearly infatuated with the man opposite; ahead, in seat No.13, sat a Countess with a poorly-concealed cocaine habit; across the gangway in seat No.8, a detective writer was being troubled by an aggressive wasp. What Poirot did not yet realize was that behind him, in seat No.2, sat the slumped, lifeless body of a woman.

How could this happen with the world's No. 1 private detective on board?