  Using scanning tunneling microscopy, we reproducibly obtained electrical
conductance spectra of superconductor- superconductor atomic point contacts
formed on various atomic sites of the substrate. From the analysis of the
subharmonic features due to the multiple Andreev reflection, spatial
distributions of the number of the conduction channels and their transmission
probabilities were obtained. It is found that the number of channels and the
transmission probabilities strongly depend on an atomic site where the contact
is formed. We also revealed how the conduction channels and their transmission
probability evolve from the tunneling to contact regimes. The Josephson current
also exhibits the atomic site dependence, which is explained by the
site-dependent transmission probabilities. Our results demonstrate a crucial
role of the atomic geometry in the conduction channels of the ultimately
confined conductor for the first time experimentally.
