A theoretical study of the conductance in a nano-scaled one-dimensional molecular device is presented. The incoherent transporting processes are included by using uniformly attaching fictitious probes (Büttiker probes) along the system. Using the D'Amato Pastawski model, we estimate the conductance of a series of one-dimensional molecular systems and analyze the dependence of the lentgh of the system on the conductance. The results are compared with those obtained with the Landauer model. We conclude that the incoherent scattering processes become dominant in long ranged electron transport.