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Sauron & Saruman are both aware that the Ring is on the move, carried by a hobbit. both have their vision on getting the Hobbit & Ring, and both believe that it is either on its way to Minas Tirith ro Rohan- and both FEAR that if it gets into the hands of another leader- that it is that leader they will have to fight.

Both are blind:

Gandalf says to 3 of Sauron: "That we should wish to cast him (Sauron) down and have NO one in his place is not a thought that occurs to him (Sauron) That we should try to destroy the Ring itself has not yet entered into his darkest dream.......Wise Fool!

Gandalf says to 3 of Saruman's Treachery: ..Saruman also ahd a mind to captre the Ring.....
...the Dark Lord knows that two hobbits were taken in the Emyn Muil and borne away towards Isengard...... He (Sauron) now has Isengard to fear as well as Minas Tirith.

The FEAR that both of these wizards feel is ultimately what blinds them, in their fear they both focus outward and to 'strength': thus Saruman misses the advance of the Ents, and Saron -looking out- doesn't see a couple little men trying to 'enter' Mordor.

Interesting that their own striving for power prevents them from seeing anything that NOT motivated by power, and in being so focused, they overlook the very things that will destroy them.
Love it!