I wouldn't ask about it, or feel the need that you need to know that part of their life in order to remain in contact. They would have shared the details if they wanted to. Many people only share the ugly side of divorce with people they are extremely close too, like close family, and sometimes they don't even then. Since it has been a while, they likely don't want to reopen taht chapter of their lives.
It really isn't your business as to why they divorced. If you really need them to know they have your support, you can always say in a very casual and friendly way, "Oh my goodness, Sharon, I must have missed that you and Mike are no longer together! You and your new boyfriend look really cute together though. If you ever want to catch up on the details, I'm always here to talk, I feel bad I wasn't there to support you during that time, but I hope it all turned out okay at least. How are you otherwise? Your kids have gotten so big!"
But really, why put an ultimatum of a very personal thing to stand in the way of any further rekindling of a friendship? I would just let it go, it really isn't any of your business anyways.And yes, you are nosey :)