Generate array of floats within possible MAX and MIN

I'm trying to generate floats however not within [0-1) but sys.float_info.max and sys.float_info.min. Unfortunately Python's random and Numpy random work as this way

a + (b-a) * random()

But random() does not generate small enough numbers to compete with exponent of MAX float.

print min([random.uniform(0, sys.float_info.max) for i in range(10000)])
>>2.0237842876e+304

How to generate floats from 0 - MAX(float) or MIN(float) to MAX(float)?