If they weren’t allowed to not find anything, a search wouldn’t be necessary.
The reasonableness of a search is not based upon the result of the search (which you can’t find out until after the search takes place), but upon having reasonable cause to believe that a search will produce the desired results.
There are no reasonable grounds to search anywhere for anything that would produce a result that anyone now living is guilty of helping murder Julius Caesar.
So reasonable doesn’t mean it’s certain or even possible, rather that it would be reasonable to suppose given the circumstances that something would be found. And in the US at least, that something must be a specific thing. You can’t have a reasonable suspicion that someone is a criminal and a search would find evidence of their crimes, you need to have a suspicion that they did a specific thing.
Suspicion doesn’t require evidence but it requires more than mere hunch, the most common source of suspicion is testimony - someone says they saw or heard something, and that in turn was enough to cause suspicion.
Recently saw a video of a judge dismissing a trespass charge where the police had randomly stopped the accused to ask if he was trespassing and he basically ignored them. If someone had reported him as trespassing that might have been a reasonable stop, but not being expressive in a random stop doesn’t give grounds for suspicion of trespassing. He could have been a serial killer or burglar with every right to be there, or even a totally innocent person that just didn’t want to talk to them.
In the US, this is frequently referred to as reasonable, articulable, suspicion or RAS.
The Supreme Court has said being wrong that the alleged behavior is a crime is insufficient for a 1983 suit, let alone being wrong that a search will produce evidence that someone committed a crime.