Either all three must be lying, or all three must be telling the truth, right? So wouldn't you have to discard the probabilities of them disagreeing? There woul

Either all three must be lying, or all three must be telling the truth, right? So wouldn't you have to discard the probabilities of them disagreeing? There would be a 1/27 chance of all lying, and wouldn't there only be an 8/27 chance of all telling the truth? The other 18/27 would be a mixture of lies and truths. So really, if we're just comparing the odds of those two outcomes to each other, would the probability just be 8/9 that it is raining in Seattle? Been a while since I've done anything with probabilities, so perhaps I'm way off here.