Database
[{_id:"1",tags:["aaa","bbb","ccc"]},{_id:"2",tags:["baa","aaa","aaa"]},{_id:"3",tags:["aac","cbb","aca"]},]
Query
db.collection.aggregate([{$match:{tags:"aaa"}},{"$project":{"tags":{$filter:{input:{"$map":{input:{$range:[0,{$size:"$tags"}]},in:{string:{$arrayElemAt:["$tags","$$this"]},index:"$$this"}}},cond:{$eq:["$$this.string","aaa"]}}}}},{$project:{tags:"$tags.index"}}])