Originally Posted by William Cloud Hickli

Tolkien addressed this in his various time-schemes and the documents excerpted for The Hunt for the Ring in UT. Apparently Sauron did *not* read his servants' minds from afar.

Sauron sent the Nine out to find "Shire" and "Baggins." he catastrophically assumed that this was near Gollum's birthplace, and the RW wasted much time combing the Vales of Anduin. The Nine only learned where the Shire was from Saruman, and in more detail from his agent (the 'squint-eyed Southerner.'). They were baffled by Frodo's detour thru the Old Forest and Strider's circitous route- they finally located the Ring again on Weathertop. But what the WK knew was *not* what Sauron knew- he only learned all this, and of the Ring's arrival in Rivendell, when the W-K made his way back to Mordor after the Bruinen (late November).

Sauron didn't pick up the trail again until messengers reached him from Moria: his response was to send out Grishnakh's force with a Nazgul to set the ambush at Sarn Gebir. The last he heard from this party, it was trailing Saruman's Uruk-hai to Isengard with two hobbit prisoners- and therefore assumed (wrongly) that either M or P was the Ringbearer, and P was a prisoner in Orthanc when he looked into the Palantir. The next hint S got was Aragorn's use of the same Stone scant hours later, and from that point Sauron was fixated on the idea that Isildur's heir had the Ring west of Anduin.