Stats test which test of the NULL that a distribution is uniformally distributed I'm looking for a statistical test which tells the probability that a given sample comes from a uniform distribution.
Shapiro test wether a sample comes from a normal distribution. I'm looking a similar test which test wether a sample comes from a uniform distribution.
Thank you
 A: You could try a Kolmogorov-Smirnov test of your data against a uniform distribution.
A: 
I'm looking for a statistical test which tells the probability that a given sample comes from a uniform distribution.

No frequentist test will tell you that probability.

Shapiro test wether a sample comes from a normal distribution. I'm looking a similar test which test wether a sample comes from a uniform distribution.

Do you mean continuous or discrete uniformity?
Is this a fully specified uniform, or one where the lower and upper limits aren't known (must be estimated)?
There are several suitable tests for fully specified continuous uniformity, including Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling. There's also the Neyman-Barton-type Smooth tests (e.g. see Rayner and Best's books and articles on smooth tests). There are other such tests. If you know likely/interesting alternatives, that helps in the choice of test.
If you like the Shapiro-Wilk, it's possible to construct a similar kind of test for uniformity with unspecified bounds. 
Alternatively, at the cost of two data points, you can exploit the properties of the uniform distribution to turn the previous fully-specified tests into tests where the bounds on the uniform are unspecified:
If $a=X_{(1)}$ and $b=X_{(n)}$ are the smallest and largest observations, just calculate $U_i = \frac{X_i - a}{b-a}$ for all the observations except you throw out the smallest and largest and test against fully-specified-uniformity on the remaining $n-2$ data values.
