Overheard on the train

Image from newtimes. NB: These are not the real protagonists of my story, which took place on the SkyTrain in Vancouver.

The two women were gabbing excitedly. I wasn't trying to eavesdrop. But suddenly, from the midst of their conversation, a strange sentence struck me.

It was uttered with a glib smoothness by one speaker, and received without dismay by the other.

"I was aware that he knew that I wasn't aware that she knew."

Though the other woman nodded with apparent understanding, I was befuddled by its bizarre intricacy. It was grammatical, but what did it mean?

For awhile I tried to unravel the meaning of this utterance. But I soon gave up. Way too confusing.
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Pulled over! Third time -- determined