right, Emmeline. You will get two contacts - one who can help with physical evidence PE - (tailor or barber or shoemaker or banker) and one (non-PE) from the other six. Its random which one, and its random when they show up. You can get one as early as your 4th or 5th favor, or you can have over 100,000 experience before you get one.
If you are subscribed, you can do cases in all four cities, and you earn contacts in each one 'afresh'. there is no advantage to one contact over another - all PE contacts are equally valuable: similarly, all non-PE contacts are equally helpful. Obviously, PE contacts are more valuable than non PE, since they will help you match physical evidence to suspects.
Sometimes, if you are in an agency, they may want to have all the contacts covered - so you may try for one, by quitting every favor that could net you the wrong one. that's a crap shoot though, and its generally more fun to take what you get.