Help with Tiger Problem using POMDP

I am trying to get a better understanding of POMDPs by trying to obtain the best policy for the tiger problem: http://www.pomdp.org/examples/tiger.aaai.POMDP

My first problem arises when I try to calculate the belief update using : b'(s') =(normalizingconstant) P(e|s') (sum.over.states)P(s'|s,a) b(s).

For the 2 horizon, my thoughts are that P(e|s') is <.85,.15> or <.15,.85> based on the evidence. Then P(s'|s,a) == 1??? (not sure if this is correct since you would always know whether you will open a door or listen?) and I am assuming b(s) for that case is <.5,.5>.

is that how I obtain b'?