I know how the system of the minigame Tears of Guthix works. My question is what would happen if both your lowest skill have the same exp?

As far as I know, one will be picked at random. Unless Jagex has some secret skill-ranking system, which I doubt.

I think that the actual exp you have is a decimal value (ex. 130342.70) as some things give 30.5 exp, not just 30 or 31. So it is probably very rare that 2 skills have the exact same exp at any one time. Or if they are tied they might raise the one that got to that exp last.