I am convinced . . . . . . . . his innocence.

The correct answer is: of.

The preposition “of” is used to express certainty or conviction about something. In this case, the speaker is saying that they are certain of the person’s innocence.

The other options are not as appropriate in this context. The preposition “by” is used to express a cause or reason. The preposition “with” is used to express a means or instrument. The preposition “at” is used to express a location or position.

Here are some examples of how the preposition “of” can be used to express certainty or conviction:

• I am convinced of your honesty.
• I am convinced of the need for change.
• I am convinced of the importance of education.

Here are some examples of how the other prepositions can be used:

• The painting was done by Picasso.
• The car was driven with care.
• The meeting was held at the office.