Inconsistent query results with and without presence of partial indexes

db.c.insert({a: [1, {c: 1}]});

db.c.insert({a: [1]});

db.c.find({"a.b": {$exists: true}}) // Returns nothing.

db.c.find({"a.b": {$ne: null}}) // Returns {a: [1]} !!!!

db.d.drop();

db.d.createIndex(

   { "a.b": 1 },

   { partialFilterExpression: { "a.b": { $exists: true } } }

);

db.d.insert({a: [1]});

const query = {"a.b": {$ne: null}};

print("Running the query " + tojson(query) + " with a partial index present");

print("Results are " + tojson(db.d.find(query).toArray())); // (1)

print("Dropping the index");

db.d.dropIndexes();

print("Results from the same query are now " + tojson(db.d.find(query).toArray())); // (2)