Given a random variable $X$ which arise from a parameterized distribution $F(X;θ)$, the likelihood is defined as the probability of observed data as a function of $θ$: $\operatorname{L}(θ | x)=\operatorname{P}(X=x \mid θ)$
In statistics, a likelihood function is a function of the parameters of a statistical model, defined as follows: the likelihood of a set of parameter values given some observed outcomes is equal to the probability of those observed outcomes given those parameter values. Likelihood functions play a key role in statistical inference, especially methods of estimating a parameter using a statistic (a function of the data).
Reference: Wikipedia
Excerpt reference: @ars's answer on What is the difference between “likelihood” and “probability”?
