Why does Hamlet believe in the ghost in Shakespeare's Hamlet?

A dash of the supernatural was expected by Elizabethan
audiences, who strongly believed in the influence of the other world.  Also, in the
Chain of Being in which the Elizabethan world found order, the king is an embodiment of
God on earth, so there is a close connection between King Hamlet and the supernatural of
which Hamlet would be aware. 

The ghost of King Hamlet is,
thus, entirely believable to Hamlet.  Further, Hamlet would give credence to the ghost
of his father since "there is something rotten in Denmark" and he suspects foul play in
King Hamlet's death.  That his father's ghost would appear to him, seeking retribution
for his murder is logical to Hamlet, the Prince of
Denmark.

Another condition of Hamlet's that allows for his
acceptance of the ghost is his sensitive and pensive nature.  Certainly, a person who is
given to much existential examination allows for the influence of other circumstances of
existence.  Not only does Hamlet perceive the ghost and hear it speak, but he feels its
presence, as well, as he proceeds through his examinations of conscience and ponderings
of the value of life.