So, your conception of justice is a process. That explains a lot. In my view, the process is only relevant to the degree that it produces (or is likely to produce) a just result. If the paladin held a quick trial or inquisition, it would not change the justice of the result. Condemning the innocent or releasing the guilty would both be injustice. (As a side note, how good would the trial have to be in order for you to consider it justice? Would the tiefling need a lawyer? Would the tiefling need a jury with no previous knowledge of the case? Or could the paladin in question act as judge and jury then act as executioner?)