Expected utility is usually written for actions, but it can be written as in the post as well, it’s formally equivalent.
However, the ratios of the conditional probabilities of those outcomes, given that you take a certain action, will not always equal the rations of the unconditional probabilities, as in your formula.
However, the ratios of the conditional probabilities of those outcomes, given that you take a certain action, will not always equal the rations of the unconditional probabilities, as in your formula.