[Mithadan]

Let's try to add some flesh to the bones here by continuing with the "What did Sauron know" theme and adding "What did Sauron suspect"?

Sauron knows that the last person who definitely had the Ring was Frodo due to the escapade at the Prancing Pony and the incident at Weathertop. He knows Frodo got to Rivendell. At this point, perhaps he is concerned that Elrond will claim it. But months pass without any sign of this happening. He knows Gandalf was involved. Gandalf encountered the Nazgul on Weathertop. He learns Gandalf has left Rivendell and learns generally the composition of the Fellowship due to the events in Moria. So Elrond has not claimed the Ring and Gandalf is not touching it. A group is heading south accompanied by Gandalf. Hobbits are in the group. Sauron's reasoning probably is as follows.

Gandalf is afraid to claim the Ring and Elrond has rejected it. It is going South. To where? Gondor is the logical destination. The Ring is being concealed. A Hobbit had it. Hobbits are weak and allowing a Hobbit to bear the Ring would present the least threat to the West. So a bodyguard is provided for the Hobbit to assist him in bringing the Ring to Gondor.

The Orc raid on Amon Hen specifically targets Hobbits. If Sauron only wanted intelligence it would suffice to capture any member of the Fellowship, not just Hobbits. If he wanted a Hobbit just to "play" with, he could have gotten one from The Shire. Grishnakh knows about the Ring. Sauron clearly thinks the Ring has remained with Frodo. So when a Hobbit is apparently captured by Saruman and (to Sauron's mind) intentionally revealed to him through the Palantir the only logical conclusion is that Sauron believed Saruman had captured the Ring.