3 inches in diameter and no hair/fur around entry/exit at all? No tracks? I'd probably set the live trap inside the run so the edge of the open door is just above and nearly touching breach in fencing. I'd cover the entire trap with dark cloth (over the entire trap - unsprung door and all). Make sure whatever it is enters trap and can't just enter run and wander `'round' assessing other weaknesses.
Let us know what the vermin is (I'd guess coon, but...).
Let us know what the vermin is (I'd guess coon, but...).