Here’s a counterexample. There is an urn filled with lots of balls, each colored either red or blue. You think there’s a 40% chance that the next ball you pull out will be red. You pull out a ball, and it’s red; you put it back in and shake the urn. Now you think there’s a 60% chance that the next ball you pull out will be red, and you announce this fact and bet on it. You pull out one more ball, and it’s blue. If you hadn’t seen that piece of evidence, your prediction would have been more accurate.
Here’s a counterexample. There is an urn filled with lots of balls, each colored either red or blue. You think there’s a 40% chance that the next ball you pull out will be red. You pull out a ball, and it’s red; you put it back in and shake the urn. Now you think there’s a 60% chance that the next ball you pull out will be red, and you announce this fact and bet on it. You pull out one more ball, and it’s blue. If you hadn’t seen that piece of evidence, your prediction would have been more accurate.