Secrets of the Empire are a semi-rare drop from all bosses in the Throne of Thunder or the eight first bosses in Siege of Orgrimmar in all difficulty levels. The chance for the item to drop is one attempt per eligible boss, per week across all difficulties, and the chance for the item to drop is the same regardless of difficulty mode. Lei Shen and the Sha of Pride have a 100% drop rate.
Much like with the [Sigil of Power] and [Sigil of Wisdom] back in Patch 5.0, in all difficulty modes, secrets are personal loot, meaning that each member of the raid has an individual chance to loot one copy. Additionally, players only have one chance at a secret per boss, no matter the difficulty mode. Thus, if players kill a boss in Raid Finder, then later turn around and defeat it in Normal or Heroic mode, only the Raid Finder kill will be eligible to drop a quest item.
^Daxxarri 2013-03-21. Secrets of the empire. LFR or Normal/Heroic?. Archived from the original on 2013-03-20. “Everyone has a personal chance to receive a Secrets of the Empire drop on Normal/Heroic; the quest loot functions the same way that the Raid Finder version of the Legendary quest did prior to 5.2.”