I feel like this is left as an exercise to the reader and no proof is needed. Bettors in a prediction market are not divine speculators causally divorced from the real world. They are embedded, and when there are a lot of them and their financial incentives are towards a particular outcome, they might act in ways that aggregate to a greater likelihood of the event transpiring than in the counterfactual setting where they are pure observers of the simulations waging in a vacuum. It seems to me there are multiple ways to formalize and prove this and this contributes to my perception the original comment seems self-evident. If that is not the case then something is wrong in my intuition.