  The Bessel point process is a rigid point process on the positive real line
and its conditional measure on a bounded interval $[0,R]$ is almost surely an
orthogonal polynomial ensemble. In this article, we show that if $R$ tends to
infinity, one almost surely recovers the Bessel point process. In fact, we show
this convergence for a deterministic class of probability measures, to which
the conditional measure of the Bessel point process almost surely belongs.
