We performed scanning tunneling spectroscopy measurements on suspended single-walled carbon nanotubes with independently addressable source and drain electrodes in the Coulomb blockade regime. This three-terminal configuration allows the resistance to the source and drain electrodes to be individually measured, which we exploit to demonstrate that electrons were added to spin-degenerate states of the carbon nanotube. Unexpectedly, the Coulomb peaks also showed a strong spatial dependence. By performing simultaneous scanning tunneling spectroscopy and electrical transport measurements we show that the probed states are extended between the source and drain electrodes. This indicates that the observed spatial dependence reflects a modulation of the contact resistance.