This area is not exactly renowned for being a hard, mechanically measurable science, so you will get many different answers as to whether this is a problem at all or not.

The wisest suggestion I've gotten with regard to this is to not fall prey to instantaneous picture. It may even be impossible to have equality in a single slice of time. Rather than looking for single point inequality, look for how the population is moving through the income inequality over time.

Basically, are the same people always in the bottom, middle, and top? If so, that's probably a problem. What's the time any given person spends in the top? Bottom? Middle?

As long as you have continuous movement throughout and no one is stuck, you can at least know that there is some semblance of equality in opportunity even if not outcomes.