The entire court of Denmark has been told that the king died

By a snake bite.

Explanation:

In the play "Hamlet", when the old King Hamlet died, rumors spread that the king died after a snake bit him.

We can find about this in Act 1 Scene 5 when the Ghost of the old King appears to Hamlet to reveal about his murder and his murderer.

The Ghost said in lines 35-40 of Act 1, Scene 5:

" 'Tis given out that, sleeping in my orchard,

A serpent stung me. So the whole ear of Denmark

Is by a forgèd process of my death

Rankly abused. But know, thou noble youth,

The serpent that did sting thy father's life

Now wears his crown." (Quoted Text from Hamlet)

So, the correct answer is words spread about the murder of the king that he was bit by a snake and died.