The distinction is simple: The probability that an event will occur is the fraction of times you expect to see that event in many trials. Probabilities always range between 0 and 1. The odds are defined as the probability that the event will occur divided by the probability that the event will not occur.

What is the difference between odds and probability? - FAQ 1466

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A probability must lie between 0 and 1 (you cannot have more than a 100% chance of something). Odds are not so constrained. Odds can take any positive value (e.g. a !T probability is the same as odds of 2/1). If instead we use odds (actually the log of odds, or logit), a linear model can be fit.

Why Statisticians Like Odds - Statistics: Data Science, Analytics ...

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