How does Shakespeare present magic in Macbeth?

In Macbeth, magic appears as a force that shapes the events of the play. The title character meets three witches after winning a battle, and they predict that he will become King. Later, after Macbeth has ordered his friend Banquo to be killed, Banquo's ghost appears to Macbeth during a feast.
These magical beings are presented as unnatural and 'other', and are set up in opposition to the natural order of courtly life. Crucially, however, it is left ambiguous whether or not magic actually exists in the play - it is possible that these are simply symptoms of Macbeth's madness. For instance, he is the only dinner guest to see the ghost at the banquet - his wife does not see the ghost and tells him 'You look but on a stool'.