`mdadm --detail --scan` should give you a starting point for a working config file.
You only really need the UUID without any other conditions (remove metadata, host, level, ...). You might want to add your email address so mdadm can notify you of problems the moment they occur (provided you have a working sendmail).
Code:
DEVICE /dev/sd*
MAILADDR some@domain
ARRAY /dev/md0 UUID=d8b8b4e5:e47b2e45:2093cd36:f654020d
ARRAY /dev/md1 UUID=845b2454:42a319ef:6ec5238a:358c365b
ARRAY /dev/md2 UUID=23cf90d2:c05d720e:e72e178d:414a8128
Even without a config the array might still be assembled, but it might end up with a different number such as /dev/md127. Since mdadm told you the devices were busy, most likely it was assembled already. Check /proc/mdstat.
If you are using initrd you might have to update that as well after changing mdadm.conf