You are correct to reason that the bookmaker has probably not applied the overround equally to all runners.

It's more likely that a runner's share of the overround is related to the amount of money they expect to take on that runner and given the favourite-longshot bias, your suggestion of short price favourites having a larger share of the overround seems sensible.

If you have a sufficient amount of data on bookmaker prices and race winners, and assume a specific relationship between a runner's odds and its share of the overround then you can find the parameters of that relationship which maximize the likelihood - in other words, the adjustment to the raw bookmaker probabilities that result in the most accurate predictions of the winners.