  A miniature Hall sensor array was used to detect magnetic induction locally
in the vortex states of the $\beta$-pyrochlore superconductor KOs$_2$O$_6$.
Below the first-order transition at $T_{\rm p}\sim 8$ K, which is associated
with a change in the rattling motion of K ions, the lower critical field and
the remanent magnetization both show a distinct decrease, suggesting that the
electron-phonon coupling is weakened below the transition. At high magnetic
fields, the local induction shows an unexpectedly large jump at $T_{\rm p}$
whose sign changes with position inside the sample. Our results demonstrate a
novel redistribution of vortices whose energy is reduced abruptly below the
first-order transition at $T_{\rm p}$.
