What is your spellcasting ability when casting a spell from a Ring of Spell Storing?

The Ring of Spell Storing states (emphasis mine):

[…] While wearing this ring, you can cast any spell stored in it. The spell uses the slot level, spell save DC, spell attack bonus, and spellcasting ability of the original caster, but is otherwise treated as if you cast the spell. […]

So say somebody has acquired such a ring and casts counterspell or dispel magic using it, or is targeted by the Arcane Trickster Rogue’s Spell Thief feature:

[…] If it is casting a spell of 4th level or higher, make an ability check using your spellcasting ability. […]

[…] For each spell of 4th level or higher on the target, make an ability check using your spellcasting ability. The DC equals 10 + the spell’s level. […]

[…] Immediately after a creature casts a spell that targets you or includes you in its area of effect, you can use your reaction to force the creature to make a saving throw with its spellcasting ability modifier. […]

What would “your” or “its” spellcasting ability modifier actually be? Do you use the modifier of whoever put that spell into the ring? Does anything change if you have levels in zero, one, or two classes that can cast spells?

Some related questions:

  • What is the spell attack bonus and spell save DC of a Thief using the Use Magic Device feature?
  • What is the spellcasting ability of a Barbarian Totem Warrior?
  • For the Ring of Shooting Stars, what is the spell save DC of Faerie Fire?
  • What is the spell save DC for this magic item from Waterdeep: Dungeon of the Mad Mage?
  • What is the Wand of Paralysis' Saving Throw?
  • Do racial/feat/non-Spellcasting classes' spellcasting abilities count as a spellcasting ability for Staff of Power?

I believe my question is a bit different from these previous ones because the Ring of Spell Storing explicitly says that the spell uses the original caster’s spellcasting ability and not the spellcasting ability of whatever creature is actually using the ring.