Probabilistic likelihood model

In simple terms a probabilistic likelihood model is a mathematical model which gives the probability of some observation (data) for some stated mathematical model capable of predicting said data as an outcome (observation). It is typical denoted as p(D|M) which is simply the conditional probability for the data D given some model M. In parameter estimation it often written as p(D|a) where a is a mathematical parameter of the model class M which would then indicate a family of associated models which only differ by the value of the parameter, e.g., a family of models which give the likelihood (probability) of observing a coin flip of heads, where the parameter a would indicate different possible weightings of a coin which would change the odds of it landing on heads in an unbiased flip.