7. From the non-empty subsets of the set $\{1,2, \cdots, 2017\}$, the probability that the sum of the elements of a randomly chosen subset is odd is $\quad$ - $\qquad$.
7. $\frac{2^{2016}}{2^{2017}-1}$.

The set $\{1,2, \cdots, 2017\}$ has a total of $2^{2017}-1$ non-empty subsets, and the number of subsets with an odd sum of elements is exactly the sum of the coefficients of the odd powers of $x$ in the expansion of the function
$$
f(x)=(1+x)\left(1+x^{2}\right) \cdots\left(1+x^{2017}\right)
$$

which is
$$
\frac{f(1)-f(-1)}{2}=2^{2016} \text {. }
$$

Therefore, the required probability is $\frac{2^{2016}}{2^{2017}-1}$.