Generally we use the term real to refer to objective claims and consider subjective claims not to be real. You can certainly use the term real in a broader sense if you'd like. I don't think the concept of reality is particularly useful or coherent, but to the extent others use the term, probability is not real in the sense it's being used in.

Nitpick on definition of "real" and "objective" follows. Proceed at your own risk :-)

Would you agree that given exact info of conditions one can objectively assign concrete probability? That would give objectivity to it.

Definition of "real" for daily life is hard (impossible?). I would say "probabilities" are as real as other useful constructs that impact our lifes. Examples would be "countries" and "laws".

Is country X real? (what if it is recognised only by 1 UN nation?) Is law real? Is law real in <insert-country-in-turmoil-with-very-very-selective-enforcement>.

I could say "I have a job!" and that statement would be true, but only with the information I currently have available (what if my boss has already decided to fire me but I've just not received the information yet?). So the statement being true is based on my information about the world, just like probability.

Are particles on the quantum level real or just mathematical constructs that describe what we can observe, just like probability is?

Sure, it's as real as those other examples, i.e. not particularly except insofar as it affects peoples' expectations.

I don't think "exact info of conditions" is objective or coherent. This pre-supposes there's an external universe with exact conditions that produces our experiences, but there's no way to distinguish this possiblity from other possibilities (like a multiverse, for instance.) This lack of ability to distinguish, in my ontology, makes the distinction meaningless. Yours may differ.