If Law Enforcement can arrest an Escort or client without reason or probable cause, without any mention of sex or sex for money whatsoever(in both the ads and in person), then why do papers/magazines/the yellowpages, still advertise them?

For which we should all give great thanks to the fathers of the this august document.

While Mr Fisher is correct as usual, his answer does not go quite far enough.  A publication such as a newspaper or magazine may have civil liability for publishing ads that foster criminal behavior, but really can't be stopped from running the ads due to the 1st Ammendment.

Many years ago 'Soldier of Fortune' magazine was successfully sued regarding a 'hit man' that was hired from some ads in the back of the magazine.  While the language in the ad was coded to not overtly state what the person was saying they were willing to do, the court ruled that the implication was strong enough that the magazine should have not run the ad.  
This doesn't really have much to do with the original question as 'the hobby' is usually a misdemeanor and SOF was sued for abetting a homicide, but I thought it interesting.

FYI, the magazine publishers settled the lawsuit for peanuts (much less than the court judgement) as they simply told the suing party that if they didn't accept their cash offer, SOF would simply declare bankruptcy and they could take over their assets (a few desks, typewriters and other office equipment) and the publishers and authors would simply open a new, identical magazine.  

MVR

You could have the world's most actionable case, with grave damages to boot; but if the defendent has low or limited assets, you're still up the creek without a paddle.

Your question about why the ads still run has been well answered already.  
LE can arrest but only for cause (real or fiction is for a court to decide).  Prostitution is generally a misdemeanor, and state statutes do vary.  But typically, a LEO has to witness a misdemeanor (or you have to confess to it, STFU!)  
LE trying to make a case on an ad, or a phone call from a hobby phone, or an e-mail...  just is not enough to be worth their while.  LE wants you to say or do something incriminating...  in the presence of an undercover LEO.  There is no question about them making the case, they get the deterant effect from the publicity with minimum man/woman hours.