Eyewitness testimony is a legal term. It refers to an account given by people of an event they have witnessed.
Eyewitness testimony is the account a bystander gives in the courtroom, describing what they perceived happened during the specific incident under investigation.
Scott Fraser studies how humans remember crimes -- and bear witness to them. In this powerful talk, which focuses on a deadly shooting at sunset, he suggests that even close-up eyewitnesses to a crime can create "memories" they could not have seen. Why? Because the brain abhors a vacuum.
An expert witness, professional witness, or judicial expert is a witness who, by virtue of education, training, skill, or experience, is believed to have expertise and specialized knowledge in a particular subject beyond that of the average person, sufficient that others may officially and legally rely upon the witness's specialized (scientific, technical, or other) opinion about an evidence or fact issue within the scope of his expertise, referred to as the expert opinion, as an assistance to the fact-finder. See here for the official federal rules.
Here's an article about expert testimony.
Inferring probabilities from track record: See Wesley Salmon’s classic text The Foundations of Scientific Inference (University of Pittsburgh Press, 1966).