I have met a lot of famous musical artists in my time and one thing they all had in common was humility. Humility does not mean a lack of confidence. They were confident but humble, those two qualities can coexist and I find it really sexy.
During my days on the stage, it was easy to fall victim to an inflated ego with people all around you always telling you how great you are, but when I would see how much talent is really out there it was easy to feel humbled again.
I, like you, have not thought of music as a competition, but do strive to get better each time I play in a sort of competition with myself, pushing me to improve. I've always believed that the largest room in the world is the room for improvement and the more I improve the larger the room gets.
I agree that being humble and believing are not incompatible.
I was sort of thinking about my reply and realizing I was not quite right
I really don't "compete" with myself either, it's more a challenge...
I keep on learning