Using ab initio molecular dynamics, the atomic structure and transport properties of eutectic Ga-In and Ga-In-Sn are investigated. The Kubo-Greenwood (K-G) and the Ziman-Faber (Z-F) formulations and the Wiedemann-Franz (W-F) law are used for the electrical and electronic thermal conductivity. The species diffusivity and the viscosity are also predicted using the mean square displacement and the Stokes-Einstein (S-E) relation. Alloying Ga causes more disordered structure, i.e., broadening the atomic distance near the In and Sn atoms, which reduces the transport properties and the melting temperature. The K-G treatment shows excellent agreement with the experimental results while Z-F treatment formula slightly overestimates the electrical conductivity. The predicted thermal conductivity also shows good agreement with the experiments. The species diffusivity and the viscosity are slightly reduced by the alloying of Ga with In and Sn atoms. Good agreements are found with available experimental results and new predicted transport-property results are provided.