Maybe. It depends on whether the model successfully describing the relationship between the three probabilities is simply due to them having to sum to 100% (i.e. describing the complete set of possibilities), or whether it's because it describes some kind of "natural law" of decision-making.

In either case, it might not be useless. Check out this chart:



As can be seen, the greater the difference in odds between the most-preferred and least-preferred horses (i.e. by how much the former is preferred to the latter in a pairwise comparison, the horizontal axis), the greater the difference between what the model predicts (the dots) and what the odds actually indicate.

While possible that it's due to the model being incorrect, I personally think it likely it's the fave-longshot bias in effect: the odds of the outsider are shorter than what the market truly believes (as it's "only" a 3-horse race) and/or the favourite is longer than it should be (as it's adjudged not worth the risk of actual money being bet).

The furthest dot to the right that's sitting on the line, looks kind of out of place. In that particular race the second and third favourite were of equal odds. Similarly, the other ones close to the line are when the first or second favourite are equal or very close to each other in the odds. So the rule of thumb could be: in a 3-horse race in which the runners are clearly ordered and 'spaced' in the market, bet on the favourite as you are likely getting overs. (Mind you, "overs" is only in the order of 2% or so - $1.38 vs $1.35 - you'd be much better off just shopping around for better odds).

The model could help you determine the conditions under which the fave-longshot bias is evident, rather than having to collect tens of thousands of races to measure the effect.