At first backoff race both have $0 \ldots 2^{1}-1$ backoffs:
$$\begin{array}{|c|c|c|}
\hline
A = 0,1 & B = 0,1 & \text{Win}\\
\\\hline
0 & 0 & \text{None}\\
0 & 1 & \text{A}\\
1 & 0 & \text{B}\\
1 & 1 & \text{None}\\
\\\hline
\end{array}$$
It is given that $B$ wins here.
For second backoff race:
$\begin{array}{|c|c|c|}
\hline
B = 0,1 & A = 0,1,2,3 & \text{Win}\\
\\\hline
0 & 0 & \text{None}\\
0 & 1 & \text{B}\\
0 & 2 & \text{B}\\
0 & 3 & \text{B}\\
1 & 0 & \text{A}\\
1 & 1 & \text{None}\\
1 & 2 & \text{B}\\
1 & 3 & \text{B}\\
\\\hline
\end{array}$
So, $A$ can win the second backoff race with $\text{P(A wins)} = 1/8$.
Now, we can see how things started initially where both had equal opportunity and how it shifted towards the first winner. This shows the potential of capture effect.