What is Evidence?

Questions that need to be asked and that people never answer:

a) In what sense is something an extraordinary claim? Presumably that some physical laws are being contravened? Is it being assumed that such physical laws can describe the whole of reality to arbitrary accuracy, or might such physical laws only be applicable to a certain domain e.g. like the physical laws making up classical physics only being able to accurately describe the macroscopic realm?

b) Anecdotes are not scientific evidence, but they are certainly evidence. So it depends on whether someone is saying that some phenomenon should be scientifically accepted, or whether it should make someone more inclined to believe something or even perhaps compel personal belief. So are those who claim that anecdotes are not evidence in agreement that anecdotes can be compelling evidence to believe something?