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

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):

resp.:

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 *

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Ok, you say "$y$ should be 1" and that the distribution is defined on $[0,1]$? In that case, you you can only have a uniform distribution, i.e., density $f(x)=1$ for all $x\in[0,1]$. That's because densities have to integrate to 1. Did you mean $x$ should be max 1? –  Nameless Dec 4 '13 at 19:09
I edited the question a bit. Basically I want to insert any x in a range of [0,1] and get a y which is in the range of [0,1] –  p000ison Dec 4 '13 at 19:24
So if I use a random number generator, which generates numbers from 0 to 1 I I would need to scalse my y –  p000ison Dec 4 '13 at 19:26