Convinced means completely sure of something. The doubt is gone, and you would argue the point.
It takes of, or a that-clause: convinced of his innocence, convinced that somebody had moved it. The word describes a state reached rather than one you started in, which is why convincing somebody is the work that leads to it. There is a common British understatement in not entirely convinced, which is a polite way of saying you think it is nonsense. The adjective convincing describes the argument rather than the person.
1adjectiveconvincedCompletely certain about something.
“She was convinced that the letter had been opened.”
Also accepted in games: certain