Ah, but it is incredible how often things force one to do the thing one would like to do. - Agatha Christie

The impossible cannot have happened, therefore the impossible must be possible in spite of appearances.

"And yet," said Poirot, "suppose an accident-"
"Ah, no, my friend-"
"From your point of view it would be regrettable, I agree. But nevertheless let us just for one moment suppose it. Then, perhaps, all these here are linked together - by death."

For in the long run, either through a lie, or through truth, people were bound to give themselves away …