The precise meaning of "probable cause" is somewhat uncertain. Most academic debates over the years have centered around the differences between "more probable than not" and "substantial possibility". The former involves the elements of certainty and technical knowledge. The latter involves the elements of fairness and common sense. There's more adherents of the latter approach, but how do you define common sense. Supreme Court case law has indicated that rumor, mere suspicion, and even "strong reason to suspect" are not equivalent to probable cause. Over the years, at least three definitions have emerged as the best statements:
Probable cause is where known facts and circumstances, of a reasonably trustworthy nature, are sufficient to justify a man of reasonable caution or prudence in the belief that a crime has been or is being committed. (reasonable man definition; common textbook definition; comes from Draper v. U.S. 1959)
Probable cause is what would lead a person of reasonable caution to believe that something connected with a crime is on the premises of a person or on persons themselves. (sometimes called the nexus definition; nexus is the connection between PC, the person's participation, and elements of criminal activity; determining nexus is the job of a judicial official, and it's almost always required in cases of search warrants, not arrest warrants)
Probable cause is the sum total of layers of information and synthesis of what police have heard, know, or observe as trained officers. (comes from Smith v. U.S. 1949 establishing the experienced police officer standard)
No offense, but your definition of probable cause is probably a lot tighter than the courts have held and your 168 is a prescription for dead citizens and free terrorists.
None taken. My definition might be tighter, but I think on this issue the courts have been pretty strict themselves. I've read cases thrown out based on bad warrants and the like. I'm certainly not knowledgeable enough to make a good argument one way or the other, though. Don't know enough about various rulings.
As for my #168, what do you dislike about it? The current method hasn't exactly worked to perfection, and I suspect if it didn't work the first time (when the police had some element of surprise) it never will.