  This paper presents the exact expressions of the transition probabilities of
some non-determinantal Bethe ansatz solvable interacting particle systems: the
two-sided PushASEP, the asymmetric avalanche process and the asymmetric zero
range process. The time integrated currents of the asymmetric avalanche process
and the asymmetric zero range process are immediate from the results of the
asymmtric simple exclusion process.
