Imagine what the result is if we're wrong about Hans. He is an extraordinarily smart person, a valuable member of society, and could have made significant accomplishments in the next 25 years with his intelligence and experience. If we're wrong then we're throwing away his future contributions to society, depriving people that he would have helped of his assistance, stealing him from his friends, and in general not allowing him to have a positive effect on anyone's life for the next 25 years. Admittedly, in the grand scheme of things, that isn't too horrible, but it would certainly be horrible for the people that he would have had a good effect on. Perhaps he would have inspired some child to go on and do great things. We can't know.
Based on that, if a person is to be imprisoned for a huge portion of his life then there should be no doubt about his guilt.
It's true that it's impossibly unlikely that Nina made herself vanish, but consider that someone else could have used her to frame him.