Option 1: Let the serial killer-rapist go free. You know they will continue harming others, but you do not take any life yourself.
Option 2: Execute a 100% innocent man in public. The man is certainly innocent, and your action will end an innocent life for no reason other than this choice.
Which do you choose and why?
Easy.
Option 1 - nothing in your rules specify that I (or somebody else) can’t “fix” the problem posed by the “serial killer-rapist” straight after I set it free.
There is no way to fix Option 2 after it has occured.