The concepts of extravalence and extracontextuality are very useful to spell out the role of contextuality in quantum mechanics, that is not non-contextual (like classical physical would be), but not either fully contextual, since modalities belonging to incompatible (non-commuting) contexts may be connected with certainty. Starting now from extracontextuality as a postulate, the fact that certainty can be transferred between contexts, and is then associated with a given projector, is the very basis of the hypotheses of Gleason's theorem, and thus of Born's rule. Also, associating a state vector with an extravalence class clarifies its status as a mathematical tool to calculate probabilities connecting modalities, which correspond to the actual observed physical events or results. This point of view is quite useful, and it can be used everywhere in quantum mechanics.