What was the Sherlock Holmes principle? 'Once you have discounted the impossible, then whatever remains, however improbable, must be the truth.'
I reject that entirely. The impossible often has a kind of integrity to it which the merely improbable lacks. How often have you been presented with an apparently rational explanation of something that works in all respects other than one, which is just that it is hopelessly improbable? Your instinct is to say 'Yes, but he or she simply wouldn't do that.'

Ch. 14, p. 169 - The Long Dark Tea-Time of the Soul (1988)