The evidence of the sailors' innocence is pretty overwhelming. It includes the confession of a man who had ties to the victim, had a history of sexual abuse against women, and who was a match to DNA from the crime scene. None of the four sailors' DNA matched that taken from the crime scene, nor did any other physical evidence.
So why were they convicted? False confessions. Prosecutors initially planned to try seven sailors, but ended up trying only four when the other three wouldn't confess. One of the convicted served his sentence and has been released. The other three are serving life sentences. The cops apparently pulled a confession out of one sailor, then used that false confession and the threat of the death penalty to get false, conflicting confessions from three others.
People still seem to have a hard time believing that false confessions happen. If the cops in this case could elicit four of them from four enlisted Navy men, it shouldn't be hard to imagine how they could get one from, say, a 13-year-old kid, or someone with a mental disability. The case is also another argument for videotaping police interrogations.