The selection weight cancels the white fraction

Let $U_1,U_2,\dots ,U_6$ be 6 urns such that urn U_k contains $3k+k^2$ balls, out of which 3k are white balls and $k^2$ are black balls, k = 1, 2, …, 6. An urn is selected with the probability of selecting urn U_k being proportional to (k + 3). A ball is chosen randomly from the selected urn. Then the probability that urn $U_6$ was selected, given that the ball drawn is white, is equal to