APD and psychopathy are actual diagnoses...

Moreover, people with antisocial personality disorder aren't emotionless. They're non-empathetic, meaning they have no regard for the emotions of others. Most people with APD are fully capable of feeling and expressing their own emotions.

If you want to re-define these terms to mean something other than what they actually mean, you could say that the evil emotionless, unreachable criminal is incredibly rare. That's because evil people, emotionless people, and unreachable people are all incredibly rare, so the combination of all 3 is even rarer.