As the others already mentioned. There are conventional variables to the unknowns such as $x$ for an unknown value or $P(A)$ for an unknown probability. We take them as variables and assume that they are unknown however there is a certain probability that they take some reasonable values. That is actually the reason why we define them.
Additionally in computer programming there is a term called 'NaN:=Not a Number'. That is also somehow an unknown value, However even worse, we dont have any hope that it can be as in the case $x$. They are often mentioned as Indeterminate_forms arising from $0/0$, $\infty-\infty,\infty/\infty$ etc..
There might be also another interpretation to understand an unknown probability. If you have a probabilistic model and If you have deviations from the model assumptions due to outliers or inaccurate estimation etc.., then this phenomenon is called uncertainty. In such a case you are unsure about which probabilistic model you have resulting an unknown probability.