> If I have a fair coin (parameter value) then the probability that it will come up heads is 0.5. If I flip a coin 100 times and it comes up heads 52 times then it has a high likelihood of being fair (the numeric value of likelihood potentially taking a number of forms).

Most of the top posts gave some math but to really any intuition, and ignored the poster's request for an example of where probability and likelihood differ. The above was the first I saw that was clear.