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Photoelectron angular distributions (PADs) from the liquid-water surface and from bulk liquid water are reported for water oxygen-$1s$ ionization. Although less so than for the gas phase, the measured PADs from the liquid are remarkably anisotropic, even at electron kinetic energies lower than 100 eV, when elastic scattering cross sections for the outgoing electrons with other water molecules are large. The PADs reveal that theoretical estimates of the inelastic mean free path are likely too long at low kinetic energies, and hence the electron probing depth in water, near threshold ionization, appears to be considerably smaller than so far assumed.