We report a combined solid-state (H-1, H-2, C-13,O-17) NMR and plane-wave density functional theory (DFT) computational study of the O center dot center dot center dot H center dot center dot center dot O low-barrier hydrogen bonds (LBHBs) in two 1,3-diketone compounds: dibenzoyl-methane (1) and curcumin (2). In the solid state, both 1 and 2 exist in the cis-keto-enol tautomeric form, each exhibiting an intramolecular LBHB with a short O center dot center dot center dot O distance (2.435 angstrom in 1 and 2.455 angstrom in 2). Whereas numerous experimental (structural and spectroscopic) and computational studies have been reported for the enol isomers of 1,3-diketones, a unified picture about the proton location within an LBHB is still lacking. This work reports for the first time the solid-state O-17 NMR data for the O center dot center dot center dot H center dot center dot center dot O LBHBs in 1,3-diketones. The central conclusion of this work is that detailed information about the probability density distribution of the proton (nuclear zero point motion) across an LBHB can be obtained from a combination of solid-state NMR and plane-wave DFT computations (both NMR parameter calculations and ab initio molecular dynamics simulations). We propose that the precise proton probability distribution across an LBHB should provide a common basis on which different and sometimes seemingly contradicting experimental results obtained from complementary techniques, such as X-ray diffraction, neutron diffraction, and solid-state NMR, can be reconciled.