Air carrier Captain reported a near mid-air collision with a drone while on approach to MIA.

Narrative

I was Captain / Pilot Monitoring (PM); the First Officer (FO) was Pilot Flying (PF). We were arriving at MIA via the VIICE2 arrival transitioning to the ILS 9. Weather was a scattered to broken deck with tops about 4;800 ft. MSL and bases about 3;800 ft. MSL. Visibility both above and below the clouds was excellent; 20 miles or more.Prior to arriving at the BILZZ intersection westbound we had been descended by ATC to 4;000 ft. MSL and slowed to 210 KIAS but were still following the STAR lateral track. At this point we were in and out of the clouds. About 4 miles west of (past) BILZZ we were cleared to descend to 3;000 ft. MSL and turn right heading 360 onto a base leg. We came out the bottom of the clouds into the clear about halfway around the turn. Just as we were rolling out northbound and passing 3;400 ft. MSL I observed a stationary object in the sky ahead; below; and off to our right. As we got closer it resolved into a quadcopter type drone. I estimated its altitude as roughly 200 feet below our altitude; so approximately 3;200 ft. MSL. I estimate the horizontal miss distance as less than 500 feet. I can't say how large or small the quadcopter was; but I can say I identified an orange glossy fuselage; and the 4 distinct black rotor booms. From my first sighting to us passing it was about 6 seconds. There was not time to take any evasive action; nor was any necessary. But it is clear to me that had we been on a collision course with it; we would not have been able to see and avoid such a small target in the time available from first sighting to impact.Its position would have been on the order of 4 miles SW of the GRITT intersection. The Class B airspace in that area extends from 3;000 ft. MSL to 7;000 ft. MSL and we were well within the vertical and horizontal confines of the Class B. I immediately reported the drone sighting to the approach controller who promptly altered the vectors for the aircraft behind us to give the drone location more berth. We were then turned onto a dogleg and cleared for the ILS 9 approach. Shortly afterwards we changed to tower frequency and proceeded to an uneventful landing. I do not know what other actions the approach controller may have taken after I left his frequency.Cause - Some person(s) unknown operating a drone in Class B airspace. Or the machine had lost contact with it's controller and gone rogue on its own. Keeping drones away from controlled airspace is must-do. The 'how' is beyond my expertise.