Here's some food for thought.
When Michael defeats Eldes, he invites him to keep going and try to stop Cipher's plan but also makes it clear that he doubts that Michael can beat Greevil. Which is less about doubting him and more about Greevil being crazy powerful (fair point, man has four shadow legendaries), though outcome is the same.
When Michael defeats Ardos, he also states that things are in Greevil's hands now but leaves to prepare a helicopter to escape in. He confirms that he did so after Greevil is defeated, so we can assume this is indeed what he proceeded to do after walking away from the battle with Michael.
And this in turn means that Ardos very much saw the possibility of Greevil losing and had much less faith in his father's strength. If you really wanted to, you could chalk that up to Ardos being so confident in his own strength and abilities that he assumed someone who can beat him will also be able to beat Greevil (and Eldes), though I'm not sure that's all there is to it. Yes, he is arrogant and loves to belittle others, but he can see and acknowledge when someone is strong. I'm sure he is aware that he's the weakest link in his immediate family, with both Greevil and Eldes being stronger than him.
So, aside from the "Ardos vastly overestimated his own strength and just happened to be proven right" theory, there are three more explanations I can think of right now:
Ardos was simply being careful and prepared for escape just in case
Ardos is a much better judge of Trainers and their abilities than we ever realized
Despite being loyal to Cipher and its leader, Ardos just doesn't think too highly of his father
Some of you may think that 2. would be giving him a little too much credit perhaps, but consider this: Both Eldes and Ardos acknowledge Michael's extraordinary strength and talent when he defeats them in Orre Colosseum. Moreover, the game suggests to us that Eldes is a bit of a "special" Trainer himself, with his training at Mt. Battle and the way he gives Michael advice like an Elite Four member or Champion would in the mainline games. So, if we agree that Ardos probably knows he's weaker than Eldes and that he can acknowledge when someone else is strong and we add in that it's very likely that the brothers regularly train together, we can assume that Ardos might have gotten an idea of what makes a Trainer "special" and superior to their peers, even if just subconsciously. And that he therefore actually had a better grasp of the true extent of Michael's abilities.
(Considering how Eldes appears to lack confidence and faith in himself, it's definitely not far-fetched to assume he doesn't think defeating him is that big of a deal.)
With 3., we have a bit of a spicy option. A lovely contradiction. Wouldn't that be so interesting? One brother doubts the syndicate and its ideals, but his belief in his father's power is almost absolute; the other brother fanatically believes in the syndicate and its ideals, but not so much in his father's power.
As per usual, it comes back to the question of just what these two think about Greevil deep down. Personally, I think it has something to do with Greevil favoring Eldes over Ardos (more on that here). Despite all the doubts and moral objections Eldes has, he appears to share a deep bond with his father - he is the one Greevil ultimately listens to when the brothers argue about the fate of Cipher, he calls him father, he gets through to him, he even physically reaches out to him. If nothing else, I imagine that Eldes feels on some level responsible for Greevil (I mean, he immediately attempts to parent Michael, a complete stranger, once they have a chance to talk alone, so I guess Eldes just parents everyone in his life, including his own parent).
Meanwhile, Ardos is likely to hold some sort of resentment over this, and just this once his anger is entirely valid or at least human. His relationship with Greevil is already showing some cracks. But this also shatters the illusion. Because what Greevil's more positive relationship with Eldes does, even if Eldes rationally understands that his father is doing some very wrong and terrible things, is keeping him in that childish adoration and dependency on an emotional level, especially since he isn't given the opportunity to physically remove himself, take the time to truly realize and internalize these facts about his father and rethink their relationship. Hell, Greevil even keeps Eldes with him on Citadark Isle while Ardos is out on his own. You can take this as illustrating the issue quite nicely, if you choose to view it in this context.
Greevil's treatment of Ardos has, in a way, released Ardos from his bonds a little bit - perhaps just enough for him to doubt his father more than his brother is currently capable of. Make no mistake: A parent should never favor one child over the other. It's bad parenting, it's harmful to all children involved, it causes deep issues. And at the end of the day Ardos' fanatical belief in Cipher makes it so he can't and/or doesn't act on whatever advantage this might give him on the road to freeing himself from Greevil's control (the level and magnitude of intentionally controlling and abusive behavior on his part is a question for another time, though I dare say that regardless of Greevil's intentions, he ended up putting his sons in a harmful position and family dynamic for sure).
If it's indeed the case that Ardos doubts Greevil's strength, power and level of control for reasons ultimately linked to unmet needs and resentment, we of course have to acknowledge that this isn't a wholly fact-based and rational process; if this was the sole reason behind his actions it would very much be the case that he just so happened to be proven right. But I think it was probably a combination of the things I listed: Ardos was reminded of the events of Colosseum, he wanted to be prepared just in case it happened again, he saw that Michael was an extraordinarily gifted Trainer who can handle Shadow Pokémon and he had already, on some level, begun to process that his father, no matter how rich and powerful he is, is a flawed person.