Weighted shuffle distribution at specific index (formula)

What's the probability of finding element A at index i in array R after shuffling it with a random sampling algorithm? Is there a general formula for that?

Example: Given array ['a', 'b', 'c'] and weights [3, 2, 1]:

p[a at 0] = 50%
p[a at 1] = 35%
p[a at 2] = 15%

I found this by making a simulation with thousands of shuffles.

The weighted sampling/shuffle algorithm: http://utopia.duth.gr/~pefraimi/research/data/2007EncOfAlg.pdf