The first we learn of his confidence is in his response to Iago's description of the complaint against him. He is sure that the great services he has rendered the city/state of Venice will "out-tongue his complaints." He has great confidence in his abilities and record as a general.
The second thing we learn of his confidence is that he quickly tells Brabantio that they ought not to fight things out here in the street as it would end poorly. He knows Brabantio is no match for him with the sword but he also gives Brabantio the respect he deserves and speaks soothingly to calm him and defuse the situation.