How do we know 1 + 1 = 2 ?
We step through the logic, one step at time, and at the end we agree it is a true statement. So at the end we know something is true because in the process we can remember, at each point we agreed with the logic and came to a conclusion.
So if there is a flaw in our process, we will only discover we were wrong, by finding it, and then confirming our result is now wrong. So perception is limited by the process and our memory of it. This shows how limited our interaction is with the world and how we take for granted so much, relying on processing systems to achieve our objectives, while not perceiving most of what is going on.
When we grasp the power of a true process though, we have something that is reliable enough to stake our lives on it.
So my conclusion is our confidence is in the process confirmed by our feelings after going through it, but we need to be careful we perform the process correctly.
So do we have more than the conviction ? But to me the conviction tells us everything is ok. And exams and learning show us, processes bring stability and success - and over-confidence without the correct process is just failure.