"Probability" is related to mathematics/science. "Likelihood" sounds more literary. However, in everyday speech, people use the two interchangeably. There's not much of a difference between them. If anything, I'd say that using "probability" makes the speaker sound a little smarter / more formal, whereas using "likelihood" makes one's speech sound more colloquial.

In ordinary English they are very close synonyms and are usually interchangeable. "Likelihood" is slightly plainer, "probability" is slightly more formal. Use "probability" with an actual percentage number. Otherwise I suggest using the plainer word. "They are forecasting a 50% probability of rain. Is that going to wash out the dirt road to the cabin?" "I don't think there's much likelihood of that. They are only predicting half an inch and the road was in good shape a week ago." In mathematics, in the field of probability and statistics, the words "probability" and "likelihood" are technical terms with precise and different definitions; if you are studying mathematics you need to look them up for yourself.

They are interchangeable.