Is Kirchoff's first law based on the probability that a current splits at a junction and goes either way?

I know that Kirchoff's law comes from the fact that charge is conserved at every junction of a circuit. But is it useful (and true) to think about this in terms of probabilities? As in, the probabilities that a current splits at a junction and goes in one direction or the other add up to 1. For example, suppose that a current $$I_1$$ splits into $$I_2$$ and $$I_3$$ going in opposite directions. Then $$\frac{I_2}{I_1} + \frac{I_3}{I_1} = 1$$.

Apologies if I sound rather ignorant. I'm just curious.

In some small amount of time a total amount of charge comes into the junction, $$Q_{in} = I_1\Delta t$$. In order for the charge not to pile up at the junction, the same amount of charge has to leave the junction in the same amount of time. $$Q_{out} = I_2\Delta t + I_3\Delta t$$. Since the charge in has to equal the charge out $$I_1\Delta t = (I_2 + I_3)\Delta t$$ or $$I_1 = I_2 +I_3$$.