Solution
= Solution
The <Conformal Markov property of SLE> says that, conditionally on $(K_s)_{s\leq t}$, the future hulls
$$
\widetilde K_s=(g_t-U_t)(K_{t+s}\setminus K_t)
$$
have the law of a fresh SLE in $(\mathbb H,0,\infty)$ and are independent of the past, with the usual interpretation of mapping out the old hull.