The motivation of holding these beliefs is very simple, if bad things are done by the justice system to innocent (or not particularly criminal people), then there's a chance that one day the justice system does the same to you through no fault of your own. That's an unsettling idea hence rejected.
I think this is another "just world fallacy"[1] adjacent idea running rampant in our society. You see this fallacy it pop up in a lot of "woo" self-help ideas like "manifesting" or "sending out positive vibrations" as well as things like faith or spiritual healing. The basic idea being that people get what they deserve so people who experience hardship - whether legal, medical, or social - deserve it. While people who do and think good things are safe from these forces.
IMHO, this is a kind of pathological extension of "internal locus of control"[2]. Internal locus of control is good for mental health and achievement, but once you start to project it onto other people without sufficient consideration of their circumstances things quickly get problematic.
