Draw random numbers from a custom probability density function in Julia

I would like to draw random numbers from a modified exponential distribution:

p(x) = C * a * Exp[-(a*x)^b] with C=1/Gamma[1 + 1/b] for normalization.

How can I do this in julia? Unfortunately I have only little experience with Julia and no experiences with creating custom random numbers. I would be very grateful for any help.