It's interesting and admirable you say that. I saw an NBC Dateline murder case documentary on Saturday, and it was amazing as it showed how hard it is for people who become "invested" in one particular suspect, early in a case when not much is known. When that turns out not to be the person who did it, there are many who simply refuse to accept what the evidence turns out to be saying.
In the TV documentary, it was about a trusted Hispanic farm hand Robert who was killed by a rigged bomb out in the fields where he worked. Early on, it was believed that Pete, a hot-headed son-nephew of the owner, who had had run-ins with Robert, had done it. But, he didn't really fit the profile as to the ability to having the skill to create the intricate bomb. Soon thereafter, LE began to get some taunting mail from the killer about the bomb and about killing the deceased's brother who also worked on the farm, and from it they were able to (a) find proof that the letters must have come from Paul, a cousin of Pete who also lived on the farm but had a history of major violence that had been buried legally (Pete had no criminal record and no history of violence), and (b) found DNA on the mailing that, while they couldn't get enough DNA to prove it was Paul, it was enough that definitively eliminated Pete and left Paul as the only who was a "possible" match. All the evidence pointed to the cousin, and lots of it eliminated the first guy from being possible.
The DNA evidence was not allowed at trial, since it wasn't enough to say it had to be Paul and the judge wouldn't even allow the suggestion. He also barred the testimony about his violent past, since it was a different case. Despite that, Paul was convicted, and the evidence was so compelling that the jury didn't have to deliberate very long.
But, the documentary noted, a large number of people in the small town still - without any proof, and with a conviction and a mountain of proof to the contrary - to this day believe that Pete did it and Paul was wrongfully accused, or still try to contrive convoluted ways that Pete must have been involved too (a possibility that LE examined, and found didn't fit the facts at all). It's so hard to let go, when we focus on one suspect, to adjust the focus elsewhere when the evidence goes there.