# Markov network, estimating unknown variable with multiple observations

I have this hidden markov model/network with four unknown variables $$y_{1:4}$$ with the discrete domain $$(0,1)$$ and four known observations $$y^{obs}_{1:4}$$ and a potential function $$\phi(x_i,x_j)$$.

$$\phi(x_i,x_j)= \begin{cases} 5,& \text{if } x_i=x_j\\ 2, & \text{otherwise} \end{cases}$$

Here's a visualization of the network

At last I have this statistical information $$p(y^{obs}_i = 1 | y_i = 1) = 0.95$$ $$p(y^{obs}_i = 0 | y_i = 0) = 0.99$$

I now need to compute $$p(y_1 = 1 | y^{obs}_1=1,y^{obs}_2=0,y^{obs}_3=0,y^{obs}_4=0$$). I however have not a single clue on how to do this. I'm completely new to HMM's and online formula's don't even come close this this sort of problem.