A number of law bloggers have pointed out the paragraph in a recent concurrence by Judge Danny Boggs that attempts to quantify probable cause. It's only a paragraph, but it's a pretty interesting paragraph and by a prominent judge. Boggs suggests that the threshold of probable cause is in the neighborhood of a 5 to 10 percent likelihood of evidence being found:

While courts have resisted mightily putting a number on probable cause, see Maryland v. Pringle, 540 U.S. 366, 371 (2003), at bottom a review of cases indicates that there must be some, albeit inchoate, feeling as to what kind of probability constitutes probable cause. My reading is that it does not require a belief that there is more than a 50% probability of evidence being found in a particular location. See, e.g., United States v. Gourde, 382 F.3d 1003, 1015 (9th Cir. 2004) (Gould, J., concurring) (collecting cases). If that were the case, one could never get a search warrant to search all three cars of a person for whom there was overwhelming evidence of general drug dealing, and specific evidence of a drug transaction the proceeds of which were now certainly in one of three cars in his garage, and certainly not in any of the others. However, to be more than a hunch or a supposition, in my own mind, requires a legitimate belief that there is more than a 5 or 10 percent chance that a crime is being committed or that evidence is in a particular location.

  I think Judge Boggs is wrong, and that his hypothetical is based on a simple analytical error. Judge Boggs assumes that the "place to be searched" for the purposes of a warrant to search for evidence in a car must be an individual vehicle. In his hypothetical, the drug dealer has three cars in a garage, and there is evidence in only one of the three cars. Boggs concludes that probable cause must be a low probability because the chances that the evidence is in any one car are only 1 in 3, and yet the warrant in that case obviously would be issued.

  The problem with Boggs' hypothetical is that the "place to be searched" in this hypothetical wouldn't be an individual car, or even the garage itself; the "place to be searched" normally would be the entire property that contained the garage and all of the cars inside it. The chances that evidence would be found in the place to be searched are 100%, not 1 in 3, as we know that the evidence will be found in one of the cars.

  Boggs' hypothetical provides a good reminder of how probable cause to search property is always contingent on the size and scope of the space searched. The larger the space to be searched, the higher the probability that evidence of crime exists there. If you make the place to be searched big enough, probable cause will always exist; for example, there is a 100% certainty that crack cocaine will be found somewhere in New York City. Conversely, the more you narrow the place to be searched, the less likely it is that probable cause exists; if you make the place to be searched infinitesmally small, you'll never have probable cause.

  With exceptions that need not be covered here, the key determinant of the scope of the place to be searched is the particularity requirement. Warrants must "particularly describe the place to be searched," meaning that cops can't ask for permisssion to search New York City, or the Upper West Side, or even a city block. Instead, they normally need to limit the place to be searched to a particular house and premises, or an office or group of offices. The only question is whether probable cause exists that somewhere on the property some evidence of the crime, contraband, instrumentality, or a fruit of the crime will be discovered.

  Finally, I think Boggs' estimate that probable cause means a 5% to 10% chance is pretty far off. In my experience, probable cause exists when the police have some pretty strong signals that there is really something unusual going on in the place to be searched. It's impossible to translate that into a numerical likelihood, as the police never know whether the selection of signals they have observed is representative of the whole. It's like the old poem about The Blind Men and the Elephant; the police never know what part of the elephant they're touching, so it's really hard to quantify the certainty of the evidence they have.

  At the same time, the studies I have seen indicate that about 90% of search warrants end up leading to the discovery of the evidence of crime sought in the search. This doesn't mean that probable cause requires 90% certainty, obviously, but I think it does indicate that probable cause in practice is more certain that Judge Boggs suggests.