There really isn't enough evidence to prove that he committed the crime, so it's (highly) 'improbable' that he'll be convicted.
The story includes a number of absurd 'improbabilities'. [=improbable events or situations]
The team made an 'improbable' comeback.
(..) If nine of us look at the same information and arrive at the exact same conclusion, it's the duty of the tenth man to disagree. No matter how improbable it may seem, the tenth man has to start digging on the assumption that the other nine are wrong. And you were that tenth man. Precisely. (..)2013 World War Z