Each of the three urns contains six balls with an urn containing five white balls and one black ball, while another urn contains four white and two black balls and, the remaining urn contains three white and three black balls.

One white ball is drawn at random from one of the three urns and, one black ball is drawn without replacement from one of the remaining two urns. (The balls are drawn blindly, without knowing which the identities are of the urns from which they are drawn.)

Determine the probability of drawing a white ball from the remaining urn.