The meaning I think is much stronger than しかったが無い. It expresses the fact that in certain special situations an action or event which is forthcoming is unavoidable. On the other hand although the former is used in similar situations it expresses more the idea that something always pans out in a certain way.
Coming I expect from the grammar construct 〜ざるをえない
You can also say やむにやまれず to mean the same thing.
I added my own example to show an alternative usage.
if anyone reads the above comment, be careful. しかったが無い is incorrect; the correct phrase is 仕方が無い（しかたがない）, without the small "tsu."
Can the Japanese example and the English translation be moved to the same example rather than separate? I keep getting blank questions on the grammar quiz because of the 'missing' data.