The big insight from our option classes is that you can price them without using probabilities or risk premia. Rather, we replicate. Hence, all the additional info is useless. Indeed, even if you had the probabilities, you would have needed to know the discount rate of the option, which is not the risk-free rate. The CAPM would say the beta of the option is related to the beta of the stock, which is also not given. (In fact, to use the CAPM, you'd first need to replicate anyway.)
Cheers, Martijn