but it doesn't work for non-public information that is different from market sentiments by only a degree. If you have private information that the Russian government has a 2% chance of using a nuclear weapon on Crimea (perhaps you know they will roll a 50-sided die and use them on a 1), but you can't tell whether the current market prices imply a 0% to 4% probability, you have no way of using your private information without performing a full analysis of the asset.

I disagree for several reasons:

1. your example is extremely unrealistic. When do people interested in geopolitics ever get new information expressed as a precise limiting frequency like your die example? That sort of estimate doesn't exist outside of prediction markets.
2. you are setting up a strawman when you say one needs to compare a 2% to a 4% estimate: you don't need to know the market's exact estimate, you merely need to know whether yours is lower. Usually, estimating a bound or inequality is a lot easier than estimating an exact value...

3. and specifically, by the reasoning I gave before about market efficiency, estimation is easy: when you get private information, you only need to know whether it would increase or decrease probabilities on its own. All other information is already priced in but your new information is not, by definition, and hence will shift the market price in the estimated direction, allowing you to profit.

   To make your example more realistic: you learn from an informant that tactical nuclear bombs came up at the latest private discussion of the Russian cabinet; you know that the market prices on Ukrainian/Russian assets implicitly assign some probability to the use of nukes, and hence some smaller probability that the Russian cabinet is discussing their use, but the market does not know that the cabinet actually has discussed the use of nukes; you do. Now, you may have no idea whether the market assigns 0.5 or 50% to the use of nukes, but its assignment is being done in the absence of this information about their discussion. All you have to do is decide: is the Russian cabinet discussing the use of nukes evidence for or against the future use of nukes, in a purely-evidential odds or decibel Bayesian sense, independent of priors or posteriors? If it's 'for', then whatever the market probability is (you may have no idea what it is and no ability to figure it out), it will shift upwards; and since the prices reflect the probability, you have an opportunity to short.

If there were a prediction market it would be straightforward to do so, however.

You can do the same thing with prediction markets, assuming they're big enough that you can treat them as efficient. Did you learn new information which is positive? Buy. Negative? Short. Knowing your own subjective probability is useful mostly when you suspect markets are inefficient and you can make a profit without learning any new information. (Typically, whenever I'm trading on a prediction market, I don't even try to elicit my own subjective probability, I just anchor on the market probability and look for signs of bias or ignorance.)

It's really just a question of efficiency. A market for a single asset will be less efficient than the market for that asset and 10 related questions because the information costs are lower for people who have private information that bears on those questions.

That's not what the question was. The question was whether you were right that "to express your view, you have to become an absolute expert in any of the assets in question so that you can estimate the implied probability of current market prices". Certainly, more targeted assets will make it easier to make money off targeted insights. But there's no possible/impossible distinction where you can make money off your nuke insights on a prediction market but no one can make money off the same nuke insight on equity markets.