What is the difference between probability and likelihood?

The difference between probability and likelihood lies with a subtlety in the context in which each term is usually referred. In a probability context, the parameters of the model are fixed, and the probability is a function of the data given those parameters. Thus, probability quantifies the chance of the observed phenomenon occurring in the presence of the fixed model parameters. In the likelihood context, the data is fixed, and the quantity is a function of the parameters given the data. For example, Maximum Likelihood estimation obtains estimates for population parameters by finding the values that are most likely given the observed data.