The Fourth Amendment protects a right to be free from unreasonable searches and seizures, and it specifies that "no warrants shall issue, but upon probable cause." This makes it a constitutional requirement that search warrants and arrest warrants be based on probable cause. However, the Constitution does not define "probable cause" or give any examples of what does or does not constitute PC.
That task, as well as the job of figuring out when to apply the same standard to warrantless searches and seizures, was left for the courts to perform. Therefore, our body of law explaining and applying the concept is found in U.S. Supreme Court decisions, and sometimes in lower court decisions applying Supreme Court rulings.
Over the years, the Supreme Court has tried to describe the level of suspicion that would amount to PC, but it has always done so in general wording that leaves it up to courts to apply, case by case. In a 1949 opinion, the court said this about probable cause:
"The rule of probable cause is a practical, nontechnical conception. In dealing with probable cause, we deal with probabilities. These are not technical; they are the factual and practical considerations of everyday life on which reasonable and prudent men, not legal technicians, act. Probable cause exists where the facts and circumstances within the officers' knowledge and of which they have reasonably trustworthy information are sufficient in themselves to warrant a man of reasonable caution in the belief that an offense has been or is being committed." (Brinegar v. U.S.)
The essence of this discussion is that it is not possible for judges and lawyers ("legal technicians") to assign some mathematical probability value for PC. Instead, the "technicians" must try to measure the facts of each case from a practical viewpoint and assess whether those facts would justify a reasonable officer in believing criminal activity was afoot.