Fruit of the Poisonous Tree, Coincidences in Fiction, and Human Behavior
Law & Order 101: the detectives discover evidence based on an illegal search warrant; the judge determines that since the warrant was illegal, anything coming from the warrant is also illegal.
BUT if the detectives/lawyers can prove that they would have come upon that evidence in a different, legal way, the evidence is allowed to stand. It is no longer "fruit of the poisonous tree."
I apply the same caveat to plot points that rely on coincidence, last minute revelations, or random miscommunications. The coincidence, last minute revelation, or random miscommunication results in the murderer being caught, the hero/heroine being saved, and/or the lovers miraculously changing their minds and not getting on the boat.
And I roll my eyes. Unless I decide that the outcome would have occurred anyway. Then, I let it go.
In Star Trek: Next Generation's "The Most Toys," the Enterprise rapidly figures out that Data was likely kidnapped. The clues that lead them to that conclusion are quite clever--it's a decent investigation. Still, I feel better knowing that Data's survival would have leaked back to the Federation eventually in any case (no way would the kidnapper's so-called friends not have spread rumors about his "new robot"). It's more interesting that Data strives to get away. It helps that his retrieval would probably have happened no matter what.
And the rescue of Frodo and Sam in Lord of the Rings doesn't bother me. (I've discussed elsewhere why the eagles couldn't have flown them into Mordor.) The eagles' rescue operation at the end isn't a coincidence or a sudden solution. The solution/end has already been achieved. Frodo and Sam did as they promised, and unlike Gollum, Frodo is still sane. It is already a happy ending. Tolkien simply supplied an eucatastrophic (his term) extension of mercy. There was no reason not to.
Moving on to murder mysteries . . . many of Agatha Christie's mysteries depend on split second timing. Death on the Nile remains utterly unbelievable to me. They are so many reasons why it wouldn't have worked, especially since the one murderer is not entirely committed to the cause.
However, Christie's Evil Under the Sun remains plausible. It also depends on split second timing, but if one ignores the convoluted murder, the underlying psychology of the murderers and of the victim give credence to the probability of her being murdered at some point. There is a sense of inevitability. *Spoiler* She is the kind of woman to give her money to a sociopathic con artist (and his wife) who will then use her vulnerability to lure her to a private cove and kill her.
On the other hand, I get extremely tired of murder mystery plots that revolve on the murderer letting some minor detail slip (ah, he wouldn't know that tiny little detail if he wasn't the murderer!). Why do the silly murderers confess? Don't they know how easy it is for a lawyer to explain away a slip of the tongue?
Still, if I REALLY like a story, I simply decide that the whole thing is taking place in some alternate universe where ordinary rules of probability work differently. But not because the whole thing is a dream. Some rules have to apply; otherwise the story ceases to be fun at all.