It can easily make sense.

Consider a very simple model, where each person in the country has a probability `p_i` of the chance that they vote for party A, and `1-p_i` that they vote for party B.

Now if we have access to the values `p_i` of all `n` people in the population, then probability that party A wins can be calculated as

    P = sum_{a \in {0,1}^n with |a| > n/2} product_{i = 1 to n} {p_i if a_i = 0 else 1-p_i}

(The precise formula doesn't matter, but clearly it can be computed.) Now assume that we don't have all the values `p_i`, but only the values of `k` people randomly sampled from the population. Then we can calculate `P` on these values to get an estimate of the probability that A will win the election. Our result clearly won't be exact, but we can use statistics to find values `P_1` and `P_2` such that the real value of `P` is in the range `P_1 <= P <= P_2` with high probability over the random sampling of people.

Here we have assumed an underlying random model, which has a probability, and we can estimate that probability within error bounds. We could try to calculate

    P* = sum_{way of sampling k people} (probability of sampling this way) * (probability A wins in this case)

But then we don't know how likely a certain set of `p` values is to be sampled, so we have to guess. Hence we are mixing uncertency and probability. Real statistical models have many different levels of uncertainties and probabilities like that.