\begin{array}{rcl}
P(B|A(i,j)) & = &
\displaystyle \frac{P(A(i,j)(A(i+1,j+1)+A(i+1,j-1))B)}{P(A(i,j))}
\vspace{0.5em}\\
&=&
\displaystyle \frac{P(A(i,j)A(i+1,j+1)B)}{P(A(i,j)A(i+1,j+1))}p+\frac{P(A(i,j)A(i+1,j-1)B)}{P(A(i,j)A(i+1,j-1))}(1-p)
\vspace{0.5em}\\
&=&P(B|A(i,j)A(i+1,j+1))p+P(B|A(i,j)A(i+1,j-1))(1-p).
\end{array}