None of this is "random" if the guy was stalking JonBenet and observing the house and/or the family. He could have been watching a long time...
For instance: all he had to do was sit in a grocery store/mall parking lot, watch for a certain type of family with a child to come out, follow them home and proceed to watch for days at a time.
Another possible scenario is that the Ramsey's going to GA to visit relatives...Karr sees them and becomes obsessed with JonBenet.....did Patsy's relatives put JonBenet's photo in the local paper in Ga everytime she won a contest?...that is another way he could have *found* her........just thinking out loud..
btw....I think whoever killed JB was in the house the whole time the Ramsey's were at the party...he had time to roam the house and write the kidnap letter....which I think he meant as a kidnapping, but something went wrong..