Why does Holmes believe that Moriarty is responsible for Douglass' murder?

Holmes believes that Moriarty is responsible because he is the character we'd least suspect.... the person that no one would believe committed the crime.

The greatest schemer of all time, the organizer of every deviltry, the controlling brain of the underworld, a brain which might have made or marred the destiny of nations—that's the man! But so aloof is he from general suspicion, so immune from criticism, so admirable in his management and self-effacement, that for those very words that you have uttered he could hale you to a court and emerge with your year's pension as a solatium for his wounded character.