Ashe is listed as Raminas' ninth child in the FFXII Ultimania Omega. The bangaa bartender on the airship to Rabanastre confirms that the other eight children were Ashe's brothers/Raminas' sons. They all seem to have died before the events of the game.

I assumed that Ashe gets the succession mostly because every other member of the royal family is dead. Not to mention the invasion/occupation by Archades. I'd be surprised if the usual succession protocols came into it.