In Shakespeare's Macbeth, the evidence that Macbeth uses to convince himself that he deserves the power and authority he obviously wants (to be king) comes in two parts.
First, the witches predict that he will be Thane of Cawdor and king:
All hail, Macbeth! Hail to thee, Thane of Cawdor!
All hail, Macbeth, that shalt be king hereafter! (Act 1.3.49-51)
The idea of being king may or may not be present in Macbeth's mind before these predictions, but it is certainly in his mind after these predictions. The witches predict that he will be king, and he definitely is interested in being so. This is step one.
Step two comes when the first prediction, that he will be Thane of Cawdor, comes true:
...for an earnest [a deposit] of a greater honor,
He [the king] bade me, from him, call thee Thane of Cawdor;
In which addition, hail, most worthy thane,
For it is thine. (Act 1.3.105-108)
Macbeth uses the coming true of this first prediction, as evidence that the second prediction will also come true.
Of course, the witches are equivocating (telling him half-truths, or telling him truths that can be interpreted multiple ways).
Ironically, Baquo warns him just a few lines later that sometimes "the instruments of darkness" tell us a little thing that comes true, in order to make us believe something larger will come true, and thereby doom us, but Macbeth completely ignores this, and interprets the evidence exactly as he wants to.