  We prove a intertwining relation (or Markov duality) between the
$(q,\mu,\nu)$-Boson process and $(q,\mu,\nu)$-TASEP, two discrete time Markov
chains introduced by Povolotsky. Using this and a variant of the coordinate
Bethe ansatz we compute nested contour integral formulas for expectations of a
family of observables of the $(q,\mu,\nu)$-TASEP when started from step initial
data. We then utilize these to prove a Fredholm determinant formula for
distribution of the location of any given particle.
