Understanding the physical properties of the chain-ladder Sr3Ca11Cu24O41 hole-doped superconductor has been precluded by the unknown hole distribution among chains and ladders. We use electron energy-loss spectrometry (EELS) in a scanning transmission electron microscope (STEM) at atomic resolution to directly separate the contributions of chains and ladders and to unravel the hole distribution from the atomic scale variations of the O-K near-edge structures. The experimental data unambiguously demonstrate that most of the holes lie within the chain layers. A quantitative interpretation supported by inelastic scattering calculations shows that about two holes are located in the ladders, and about four holes in the chains, shedding light on the electronic structure of Sr3Ca11Cu24O41. Combined atomic resolution STEM-EELS and inelastic scattering calculations is demonstrated as a powerful approach toward a quantitative understanding of the electronic structure of cuprate superconductors, offering new possibilities for elucidating their physical properties.