word choice - What's the difference between なぜ、どうして and なんで when meaning 'why'?

I've been meaning to ask this for a while.

What is the difference between these 3 words. I was taught they all mean "why", but obviously, being different words they convey different nuance and would be used in different situations.

What would be the difference between these 3 sentences and in what situations would they be used?

なぜここにいるのですか？
どうしてここにいるのですか？
なんでここにいるのですか？