Sherlock's Method

Sherlock Holmes claimed that "when you have eliminated the impossible, whatever remains, however improbable, must be the truth." This is the heart of eliminative reasoning — solving problems by ruling out what cannot be true rather than proving what is.

You may not know which suspect is guilty, but you can often show which ones were nowhere near the crime. What is left is not proven — it is what survived scrutiny. That is usually good enough for action, even if not for mathematical certainty.