Negative exponential/ exponential power distribution between 0 .0 and 1.0?

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Note: I'm not very familiar with distribution and higher level math

Heyho,

I'm currently looking for a way to generate random values between 0.0 and 1.0 with an exponential power or negative exponential distribution. It should look something this (but the max. y should be 1.0):

wikipedia

resp.:

enter image description here

I'm really not very familiar with this kind of math (also because I'll probably learn it in about 4-5 years :P). My main goal it to generate a value, let's say between 5 - 65, where higher values should be much more probable. Basically I want to insert any x and get a y which is in the range of [0,1] with an exponential distribution.

Related(Does not cover negative exponential distribution): Random Exponential-like Distribution

**I'm using Colt for higher level math **