Perception of probability of being right
You'd probably want to take a look at signal detection theory. This is a set of tools that you use to analyse how well a person (or an animal, or a machine) is able to discern trials where there is a signal present (e.g. a picture is shown that has been shown before, a tumour is present in an x-ray image, a dot on a radar is an enemy aircraft) from trials where there is no-signal present (e.g. a picture is shown that hasn't been shown before, a tumour is not present in an x-ray image, a dot on a radar is not an enemy aircraft).

Whether a person perceives a signal or not is not always easy to discern. There will always be a certain interplay between the hit rate and the false alarm rate (in that you for example, if you always answered "signal", would have a perfect hit rate, although your false alarm rate would be terrible), and based on a number of criterias (time pressure, instructions, reward structure et cetera) one can manipulate the response patterns of a certain individual.

There has been attempts to create models where accuracy, speed and certainty all are taken into concideration; see for example Plescak and Busemeyer (2010).