How to interpret covariance(A,B) divided by percentile rank of std dev(A)?

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Is there a way to make meaning of it? I was thinking that maybe because the covariance is divided by the percentile rank of std dev of A, the magnitude of A is to a degree bounded. But how does it change the covariance, as covariance is about the co-directions of A and B rather than the magnitude in the first place. Essentially, what does "covariance(A,B) divided by percentile rank of std dev(A)" reveal? Any thoughts would be greatly appreciated!