We have measured the spatial distribution of motile Escherichia coli inside spherical water droplets emulsified in oil. At low cell concentrations, the cell density peaks at the water-oil interface; at increasing concentration, the bulk of each droplet fills up uniformly while the surface peak remains. Simulations and theory show that the bulk density results from a `traffic' of cells leaving the surface layer, increasingly due to cell-cell scattering as the surface coverage rises above $∼ 10\%$. Our findings show similarities with the physics of a rarefied gas in a spherical cavity with attractive walls. ; Comment: 5 pages, 4 figures, Supporting Information (5 pages, 5 figures)