A： We saw a police helicopter overhead yesterday morning.
B： Really? They would have been looking for those bank robbers.
This sounds incorrect to me. Personally, I would say something like "Really? They WERE PROBABLY looking for those bank robbers." In order to use this verb tense here, you would need a situation like...
A: Our police helicopter was supposed to be out looking for those bank robbers yesterday.
B: Really? The helicopter would have been responsible for locating and apprehending them, but I hear the helicopter ran out of fuel right before the call and had to return to base.
