If Omega asked me the probability of the next bead being lilac, I would be surprised to if the next bead actually was lilac, in a way I would not be surprised to find the bead is turquoise, an event to which I assign equal probability, but was not specifically considering prior to the draw, as any higher probability set of events which excludes drawing a turquoise bead would seem artificial. If the first two beads are the colors Omega asks me about, my leading theory would be that Omega will draw out a bead of which ever color he just brought up. (The first draw would cause me to consider this with roughly equal probability as maximum entropy.)
If Omega asked me the probability of the next bead being lilac, I would be surprised to if the next bead actually was lilac, in a way I would not be surprised to find the bead is turquoise, an event to which I assign equal probability, but was not specifically considering prior to the draw, as any higher probability set of events which excludes drawing a turquoise bead would seem artificial. If the first two beads are the colors Omega asks me about, my leading theory would be that Omega will draw out a bead of which ever color he just brought up. (The first draw would cause me to consider this with roughly equal probability as maximum entropy.)