A slight expansion of the existing thread What is the difference between 「はずがない」 and 「わけがない」?, but what is the difference or use cases for when to use はずがない, わけがない, しょうがない?
On はず and わけ, answers in the original question explain it better than I would so I'll leave it to them.
But on しょうがない, it's totally different from the other two. しょうがない is used when you don't have other choice but to do it. It can also mean "there's nothing else you can do"
p/s: thanks for expanding my question