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Depends on your model choice to model place probability.
Harville (1973). Stern (1990), Henery (1981), Bacon-Shone et al (1992) Lo and Bacon-Shone (1994)
Normal probability models best fit the data, yet suffer from favorite and longshot bias. i.e. the probability of finishing first or second or third is overestimate for horses which have a high probability and underestimated for horses having a low probability of winning
There has historically been some limited success with obscure gamma ranking models as well
Fast way would be to compute Harville probabilities then adjust the Harville values based on a regression with track data.
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