What does it mean "choose one randomly"? I do not get what this sentence mean.
I have a set of numbers $\mathcal{L_{\ell}}=\{n_1, n_2, \dotsc, n_{\ell}\}$. Choose randomly one number from $\mathcal{L_{\ell}}$. 
Does it mean the probability of choosing $n_i$ is $\dfrac{1}{|\mathcal{L_{\ell}}|}$, i.e., $\mathbb{P}\left(\mathrm{choosing}\;n_i\right)=\dfrac{1}{|\mathcal{L_{\ell}}|}$?
Or, the sentence is incomplete and one must choose the distribution in order to be a correct sentence? i.e., Choose randomly with uniform distribution one number from $\mathcal{L_{\ell}}$.
Thank you for your help.

Just to make my question as answerd. I am using both comments from Sébastien and Arkamis:

It depends if the use of the word "randomly" implies a mathematical sense of randomness, or if it is used as a synonym for "arbitrary". In the latter case, one doesn't need a distribution. The point is that the choice of element is unimportant. –  Arkamis Apr 16 at 17:49

Yes strictly speaking, we HAVE to specify what is the distribution. But by convention, when this distribution is not specified on a finite set, "randomly" is understood as "randomly with uniform distribution". –  Sebastien Apr 16 at 17:51

