Both Uses

divine
in
We Beat the Street
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For some reason, he felt a glimmer of possibility, almost as if this idea had been divinely inspired.†
Chpt 21 *
"You know, Dr. Davis, your life must be guided by divine intervention," she said.†
Chpt 21

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.