The part that all these nice theories miss is that you actually do not know the distribution p(win) (in the case of Kelly) or the expected return and covariance (in the case of Markowitz).
The good news is that you don't need to know it exactly, you just need to make a better guess than the bookies (w.r.t. the Kullback Leibler divergence or cross-entropy, whichever takes your fancy).
Same goes for Black-Scholes which includes _future_ volatility.
Even if we had neither price nor volatility, we can still talk about the surface of possible (price, volatility) pairs which are compatible with the model.
The implied vol is a useful way to make sense of the actual market prices of options. We also might have some predictions about the market's implied vol changing going forward and we can reverse those errors back into expected price changes (and maybe trade on them).