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.
(..) - What's that got to do with it? You can have pancakes any damn time of night you want. - Come on, you want some breakfast? - Sure. It was an improbable romance. He was a country boy. She was from the city. She had the world at her feet, while he didn't have (..)2004 The Notebook