I think what's meant is something like p(mud_{t+1} | rain_{t}) = 1 and p(rain_{t+1} | mud_{t}) = p(rain). Say during 10 units of time it rains at points 1, 3, 4

I think what's meant is something like p(mud_{t+1} | rain_{t}) = 1 and p(rain_{t+1} | mud_{t}) = p(rain). Say during 10 units of time it rains at points 1, 3, 4, 6, and 10 and it's muddy IFF it rained in the previous period. Then the above probability statements are true and it's only muddy 40% of the time.