[Boromir88]

I agree with Inzil that probably whatever Sauron knew came from Saruman and also Sauron's reasoning that only sees others in his own skewed mind for power. Like as Gandalf tells the Council:

...the only measure that he knows is desire, desire for power and so he judges all hearts~The Council of Elrond

Tolkien wrote that Sauron was not "sincere" atheist like Morgoth became, that is he never denied the existance of Eru and the Valar...his plans to dominate Middle-earth just came about from no longer fearing Eru or the Valar getting involved in Middle-earth's problems. In HOME X: Morgoth's Ring there is more explanation that is related to how Sauron viewed the Istari:

He probably deluded himself with the notion that the Valar, (including Melkor) having failed, Eru had simply abandoned Ea, or at any rate Arda, and would not concern himself with it any more. It would appear that he interpreted 'the change of the world' at the Downfall of Numenor when Aman was removed from the physical world in this sense: Valar (and Elves) were removed from effective control, and Men under God's curse and wrath. If he thought about the Istari especially Saruman and Gandalf, he imagined them as emissaries from the Valar, seeking to establish their lost power again and 'colonize' Middle-earth. as a mere effort of defeated imperialist (without knowledge or sanction of Eru).~Morgoths Ring - Myth's Transformed Text VII

This fits with what Gandalf judges about Sauron, he can only see people through his own power-tinted goggles. If he thought about the Istari, he just saw them as some rogue emissaries sent by one of the Valar to carve out a certain sphere of influence in Middle-earth for themselves. He never appeared to think the Istari were actually sent on an Eru-sanctioned mission to bring about his defeat.

Saruman fell away from the mission to his own designs and lust for power, and this is where Tolkien gives as the reason that Sauron was always able to understand Saruman more, while Gandalf had always eluded him:

Sauron had, in fact, been very like Saruman, and so could understand him quickly and could guess what he would be likley to think and do, even without the aid of the palantiri or of any spies, whereas Gandalf elduded him~ibid

Sauron understood Saruman almost right away, because Saruman is essentially a Sauron-lite version. If Sauron drank whole milk, Saruman would be drinking skim. Gandalf was the one that eluded him, because Sauron was incapable of viewing the world without his lust-for-power goggles.