If I flip a coin 1000 times in a row and it lands on heads all 1000 times, what is the probability that it's an unfair coin? Consider a two-sided coin. If I flip it $1000$ times and it lands heads up for each flip, what is the probability that the coin is unfair, and how do we quantify that if it is unfair? 
Furthermore, would it still be considered unfair for $50$ straight heads? $20$? $7$?

In order to assign a probability to this event you need to start with a prior probability which can then be updated based on the data.  Probabilities can't really be derived from experience alone, you need to start with some sort of "inductive bias" in order to draw conclusions from evidence.
The heuristic approach of hypothesis testing gives a framework for making decisions in these situations, but it doesn't pretend to assign probabilities to those hypotheses.
