Conviction should increase after investigation, not replace it.

Conviction has a proper place in a sequence: you look into something, and then you become confident in proportion to what you found. Reversed, confidence arrives first and the investigation becomes decorative, a search for supporting material rather than a genuine inquiry. Both look identical from outside, and only one can teach you anything.

When you notice yourself already sure, ask whether you got there before or after examining it. If before, do the examining anyway, and deliberately look for the strongest opposing case. The conviction you end with may be the same and it will be worth considerably more.