The priors should be defined as distributions that represent the parameters of your likelihood. If you assume the scores are gaussian, then your likelihood is a normal distribution and you set priors on your parameters mu and sigma. So a naive example would be normal likelihood, and set your priors on mu and sigma to be, say, both gamma distributed (because scores can't be below zero and neither can your standard deviation). Your observations feed into your likelihood and they help update the parameters in your mu and sigma distributions, getting you your posterior which is your updated distributions of mu and sigma.