Usage patterns
〈人〉と偶然会うto run into someone by chance
I happened to run into a former colleague at the station.
〈物〉を偶然見つけるto happen to find something by chance
I happened to find a cute kitten in the park by chance.
〈事〉は偶然だit's just a coincidence that ...
It was a coincidence that the two of them shared the same birthday.