as an example of this, pretend probability is a velocity: https://www.mathpages.com/home/kmath216/kmath216.htm

going beyond that page, think about beta distributions (and dirichlets). they are probability distributions about probabilities. try recentering the beta distribution between -1 and 1 first (representing c).

going even further, recall the bernoulli-binomial-beta connection. treat the recentered beta distribution's parameters as bernoulli trials. try placing them in a light cone. let me know what interesting things you find ;)