With the help of the explicit expression for the semi-group of BM killed at time \(T_{0}(3.1 .9)\), deduce the semi-group of \(\mathrm{BES}^{3}\) from formula (6.1.8).

\[\begin{equation*}
\left.\mathbb{P}_{a}^{3}\right|_{\mathcal{F}_{t}}=\left.\frac{X_{t \wedge T_{0}}}{a} \cdot \mathbf{W}_{a}\right|_{\mathcal{F}_{t}} \tag{6.1.8}
\end{equation*}\]