An elderly woman on the train sees a man in another train running parallel throttling a woman to death, while he is oblivious to her watching - his back is to the window. She is thouroughly traumatised, and reports it as soon as she can at a railway station. But there is no dead woman on any train or a dead body dumped near any tracks anywhere possible where a parallel running train at that time could have stopped.
And yet - she is sure, she saw the murder taking place, was not mistaken, dreaming of hallucinating.
Fortunately she has an intelligent friend, another elderly woman, the fraile white haired Miss Marple.