  We compute the full probability distribution of the positions of a tagged
particle exactly for given arbitrary initial positions of the particles and for
general single-particle propagators. We consider the thermodynamic limit of our
exact expressions in quenched and annealed settings. For a particular class of
single-particle propagators, the exact formula is expressed in a simple
integral form in the quenched case whereas in the annealed case, it is
expressed as a simple combination of Bessel functions. In particular, we focus
on the step and the power-law initial configurations. In the former case, a
drift is induced even when the one-particle propagators are symmetric. On the
other hand, in the later case the scaling of the cumulants of the position of
the tracer becomes different than the uniform case. We provide numerical
verifications of our results.
