  We report $^{75}$As nuclear magnetic resonance studies on a very clean
hole-doped single-crystal Ba$_{0.68}$K$_{0.32}$Fe$_{2}$As$_{2}$ ($T_{\rm
{c}}=38.5$ K). The spin-lattice relaxation rate $1/T_{1}$ shows an exponential
decrease below $T \simeq 0.45 T_{\rm c}$ down to $T \simeq 0.11 T_{\rm c}$,
which indicates a fully opened energy gap. From the ratio $(T_{1})_{c} /
(T_{1})_{a}$, where $a$ and $c$ denote the crystal directions, we find that the
antiferromagnetic spin fluctuation is anisotropic in the spin space above
$T_{\rm c}$. The anisotropy decreases below $T_{\rm c}$ and disappears at $T
\rightarrow 0$. We argue that the anisotropy stems from spin-orbit coupling
whose effect vanishes when spin-singlet electron pairs form with a nodeless
gap.
