Here's why:
* Fortinbras's ambition: Fortinbras is a young prince who has been seeking to reclaim land lost to Denmark. Throughout the play, he demonstrates ambition and a willingness to use military force.
* Horatio's statement: After Hamlet dies, Horatio tells Fortinbras that "the election lights on Fortinbras," meaning he would likely become the new king.
* No other clear heir: Hamlet's own death leaves no clear successor, and there is no mention of any other claimants to the throne.
While the play doesn't explicitly state Fortinbras becomes king, the evidence strongly suggests he would be the most likely heir.