In a corpus, suppose there are $4$ words, $a,b,c,$ and $d.$ You are provided with the following counts.

$\backslash$table$[[$n$-$gram,count,n$-$gram,count,n$-$gram,count$],[$aba$,4,$ba$,5,a,8],[abb,0,bb,3,b,9],[$abc$,0,bc,0,c,8],[$abd$,0,bd,0,d,7]]$

Use the recursive definition of backoff smoothing to obtain the probability distribution, $(w_{n-2}{w}_{n-1}|),$ where $w_{n-1}=b$ and $w_{n-2}=a.$ Also assume that hat$(P)(x)=P(x)-\frac{1}{8}$