  For a class of one-dimensional determinantal point processes including those
induced by orthogonal projections with integrable kernels satisfying a growth
condition, it is proved that their conditional measures, with respect to the
configuration in the complement of a compact interval, are orthogonal
polynomial ensembles with explicitly found weights. Examples include the
sine-process and the process with the Bessel kernel. The argument uses the
quasi-invariance, established in [1], of our point processes under the group of
piecewise isometries of the real line.
