PMO 2017 Problem 2

Find all positive real numbers $(a,b,c) \leq 1$ which satisfy

$$\huge \min \Bigg\{ \sqrt{\frac{ab+1}{abc}} \sqrt{\frac{bc+1}{abc}}, \sqrt{\frac{ac+1}{abc}} \Bigg \} = \sqrt{\frac{1-a}{a}} + \sqrt{\frac{1-b}{b}} + \sqrt{\frac{1-c}{c}}$$