Database

[{_id:1,"contacts":[{userId:"John",conversation:1},{userId:"Jenny",conversation:2}]},{_id:2,"contacts":[{userId:"John",conversation:1},{userId:"Jenny",conversation:2}]}]

Query

db.collection.update({_id:1},{$set:{"contacts.$[x].conversation":3}},{arrayFilters:[{"x.userId":"John"}]})

Result