We report a precise measurement of the ratio of branching fractions B(Λ)c → pK0Sπ0)=B(Λ)c → pK−π)) using 980 fb−1 of e)e− data from the Belle experiment. We obtain a value of B(Λ)c → pK0Sπ0)=B(Λ)c → pK−π)) = 0.339 _ 0.002 _ 0.009, where the first and second uncertainties are statistical and systematic, respectively. This Belle result is consistent with the previous measurement from the CLEO experiment but has a fivefold improvement in precision. By combining our result with the world average B(Λ)c → pK−π)), we obtain the absolute branching fraction B(Λ)c → pK0Sπ0) = (2.12_ 0.01 ± 0.05 ± 0.10)%, where the uncertainties are statistical, systematic, and the uncertainty in the absolute branching fraction scale B(Λ)c → pK−π)), respectively. This measurement can shed light on hadronic decay mechanisms in charmed baryon decays.