It's equivalent to multiplying all inputs by log b. And multiplying all inputs by a value changes how much the probabilities are extremized. This is easy to see

It's equivalent to multiplying all inputs by log b. And multiplying all inputs by a value changes how much the probabilities are extremized. This is easy to see because adding a value to everything doesn't change the output, so the biggest input can be assumed to be 0 and others negative. So multiplying by 0 makes all outputs equal while as the multiplier tends to infinity, all other inputs tend to -infinity and thus the biggest output tends to 1 and others to 0. Multiplying by negative numbers results in the lowest becoming the highest.