Timeseries of odds in race - how to pick a model
Odds are directly connected to prediction accuracy. 4 means that you loose your money in 4 cases and win in one case. This is 20% probability $\left(\frac1{4+1}\right)$. If the bet goes down to 0.25 then the probability is 80% $\left(\frac1{0.25+1}\right)$. This logic is true if the spread between betting for the horse and against the horse is low. Betting is a financial market where people with the best betting algorithms bet the most and actually decide what the bet should be. If there is a situation on the market where someone could earn money it will be closed in milliseconds by trading robots. This is called an Efficient Market Hypothesis. In your data you can actually check if the hypothesis is true for horse betting.

If you would like to use ML algorithms to try to predict the outcomes better:

There are several ways to interpret the data.


You predict the probability that each horse is a winner. 
You predict a rank of each horse.
You predict time difference between horses and the winner 
You predict time


Some algorithms could be better at predicting one problem or the other. 

Possible algorithms: 


Linear regression. I always start with this because it is easy to calculate and easy to interpret. You build separate models for each horse number. Can be used for all problem definition. 
Logistic regression. Similar to regression, but can only be used for the first problem definition. 
LGBoost and XGBoost. Most likely the best models for such data, because the data is structured (not an image, sound). Can be used for all problem definitions. 
Neural networks. For example MLP (multilayer perceptron).


You can also calculate some additional features. For example, multiply some odds, or calculate inverse normal distribution from the odds.

I would also recommend to collect more data. For example weather data. Then it is good to know the horse. Some horses could be more popular than others and receive better odds. Also time of the year because the horses could have a training plan according to the time of the year.