The stretch that reflects the conflict of the person versus the unknown is "Of death, contagion, and unnatural sleep:
A greater power than we can contradict
Hath thwarted our intents."
In this passage Frei Laurence is explaining to Juliet that "a greater power" took the life of Romeo and that they can do nothing about it, because this greater power is more powerful than them.
And this is a perfect example of conflict between a person and the unknown, because until then the "greater power" which the friar was referring to was something unknown to them who are people.