Psychopaths are much more likely to commit crimes, but I got the impression most do not.
A quick google is saying UK and US prisons have about a 25% psycho population. Psychopathy: Antisocial, Criminal, and Violent Behavior -- Maier 51 (3): 394 -- Psychiatr Serv
15-25%: ScienceDirect - International Journal of Law and Psychiatry : Personality Disorders, Psychopathy, and Crime in a Norwegian Prison Population*1, *2
26%: MEASUREMENT OF PSYCHOPATHY IN A UK PRISON POPULATION REFERRED FOR LONG-TERM PSYCHOTHERAPY -- HOBSON and SHINES 38 (3): 504 -- British Journal of Criminology
I have no idea how trustworthy these sources are though.
The definitions often vary and are quite vague sometimes, as well as there being a scale of extremity. So it's hard to tell. But now to find total populations of prisons relative to the country's and an accurate assessments of the psychopath population...