I'm not sure what you mean by how do you deal with them because if the person has no doubt in their abilities and they are ok then there's nothing to deal with them about. But I'm going to guess that we are confronting somebody who claims to have no doubt in their actions, speech and thoughts and their abilities, yet maybe they are doing something that is not right. They've got a mistake in their thoughts. How do we deal with them in their total belief that they are right, have no doubt, but we can see that they're doing something wrong? There's not much we can do for this person. If they totally believe, if they are 100% certain that their way is the right way, then often we just have to walk away from them, there won't be much we can do.
If they are creating problems, of course, we try to stop them, but if it's just based on points of views and they are adamant that their way is the right way and have no doubts about it, then there's no point in trying to argue with them.
When I was in college there was a group of fellows on my swimming team who got into a religion that was called, The Way. It consisted of born again Christians and they were adamant that only the people in The Way could go to heaven, even other Christians couldn't go. They were so extreme it was bizarre. And they were absolutely defiant, absolutely certain that The Way was the only thing that would save anyone on the planet.
I just kept away from those guys. Some of them used to be close friends of mine, I just kept away from them - there was nothing I could possibly do. Years later some of them got out of it. I had a conversation with one of them who got out of it. He admitted that it was very false and was not a smart thing to do. He was lucky. Some of the other friends are still in it even today and they are certain theirs is the only way. So there's not much you can do for someone when they firmly believe that they are right and everything else is wrong.