How can Shakespeare's "Hamlet" be understood through a political lens by contrasting the appearance of the ghost in different scenes?

In Shakespeare's Hamlet the title character's father appears three times...as a ghost!

This apparition first appears to a duo of guards and Hamlet's friend, Horatio. But the ghost chooses not to speak to these three. Why?

In the ghost's second scene, he does choose to speak with young prince Hamlet. The spirit tells Hamlet of Claudius' deception. Why would the ghost speak only to Hamlet? What does this say about the politics of the play?

We know that Hamlet's kingdom, Denmark, is a monarchy. That means that political rule and power passes from parent to child. In a monarchy, rulers are considered to be divinely chosen. If their rule is broken and the divine will is not carried out, the whole kingdom suffers. Hence, "something is rotten in the state of Denmark" (I.iv). Claudius' betrayal has set the kingdom "out of joint" (I.v). 

Who is capable of putting the kingdom back in joint? Only Hamlet. If Denmark is suffering because of the interruption of rightful rule, only rightful rule can restore it. Hamlet, the prince and the murdered king's son, is the only person capable of bringing the kingdom back to political and metaphysical wholeness. 

The ghost brings a supernatural element into this political situation. By speaking only with Hamlet, the ghost puts the whole kingdom's political future solely into the hands of the person who can save it.