The Google definition is
odds, plural noun:
the ratio between the amounts staked by the parties to a bet, based on the expected probability either way.
Notice that the definition is the ratio (as in, there is by definition only one ratio). So, even though the noun odds is plural, when you replace the word with it's definition, it would switch from "What are the odds?" to "What is the probability?"¹. While odd is a word with its own definition, you cannot use it as a singular form to odds. It's similar to the word clothes; you wear clothes, but you do not say that your pants or shirt are each a cloth.
¹ Odds (ratio) and probability are different but related terms in statistics, but when using them in a non-statistcal context, they are generally interchangeable.