Let's say that you are put on trial for a murder that you didn't commit. And then let's say that you are convicted of that murder. And let's say that you appeal your conviction but the conviction is upheld because the judge, lawyers, and jury in your case all acted appropriately. The facts and testimony made it look like you were guilty, but you weren't. It wasn't the fault of the justice system that you were convicted, but the fault of a cruel twist of fate.
That can happen. I am sure it has happened many times.
So, imagine now that you are put on death row. And while you are awaiting your execution, the witnesses at your trial begin to recant their story. Eventually, seven of the nine key witnesses against you recant their testimony. New people come forward and implicate one of the witnesses against you as the true murderer.