Not for shaving, but close relative.

I bought an antique grooming set that has Ebony handle hair and clothes brush (how do i tell which is which? one is long and skinny, other shorter and fatter, bristles look basically the same)

Both seem to be in good shape, bristles aren't breaking/falling out, so i think it just needs a good cleaning. How would I go about doing this?

Kit looks similar to this, only arranged a bit different