It happens all the time, way too often.
I was in pre-law when swayed over to follow the "family" plan but still love and am fascinated with the criminal mind. I am still grabbing any true crime scenario books I can get my hands on.
Many of the people are given the most harsh sentences allowed yet, still through overcrowding, time off for good behavior, etc, yet still get out far sooner than anyone at those trials could have begun to imagine.
The prison systems really offer little in the means of rehabilitation so someone who was already violent and socially inept is now a thousand times less able to be a productive member of society, therefore most reoffend. Ironically, those found guilty of crimes that they didn't commit who have been cleared due to DNA evidence often find themselves back in the prison system relatively quickly. Keep in mind that in most of these cases though, they were not "innocent" men, innocent of the charges pinned on them but living in the fast lane none the less.
Many of our most notorious serial killers and serial rapists have been incarcerated previously.