All 3 Uses

divine
in
The Epic of Gilgamesh
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Gilgamesh shouted, "By the life of Ninsun my mother and divine Lugulbanda my father, ..."
Book 2 *

divine = or god-like
By the life of my mother Ninsun who gave me birth, and by the life of my father, divine Lugulbanda, let me live to be the wonder of my mother, as when she nursed me on her lap.†
Book 2
A second time he said to him, 'By the life of Ninsun my mother who gave me birth, and by the life of my father, divine Lugulbanda, until we have fought this man, if man he is, this god, if god he is, the way that I took to the Country of the Living will not turn back to the city.'†
Book 2

Definitions:

(1) (divine as in: to forgive is divine)
wonderful; or god-like or coming from God
(2) (divine as in: divined from tea leaves)
to discover or predict something supernaturally (as if by magic)
(3) (divine as in: divined through intuition)
to discover or guess something -- usually through intuition or reflection
(4) (meaning too rare to warrant focus)
In the time of Shakespeare, divine was sometimes used as a noun to reference a priest or a person of the church.

Divinity typically refers to a god or to a school of religion, but on rare occasions, it refers to the name of a kind of soft white candy. To remember that sense, you might think of it as tasting divine/wonderful.