This is from the BBC, Shooting of 3 women shocks Italy
"Shooting of 3 women at a cafe shocks Italy."
When I read the headline, I can guess the meaning from the context. Someone else did the shooting at 3 women.
But grammatically, the structure "Shooting of 3 women..." sounds ambiguous to me when I read it first, because it could sound like "the shooting which was done by the women .....", because "of" creates a meaning "the shooting belongs to them" and the word "shooting" is a noun. Then the "shooting of 3 women" sounds like "the shooting (activity) which belongs to the 3 women".
I am not quite sure if this is ambiguous in English Language. That is why I am asking.
And secondly, if I want to tell about another happening in which "3 women shot at someone else", how will I structure the question. Should I say "shooting BY 3 women..." or should I say "3 women's shooting......"