Function for a series of numbers like Normal/Laplace Distribution function

Question

I have a series of numbers like in this CSV file that I'm trying to find a fit function for it to find priori.

Rule 1: I should add that $\mu$ is $0$ and $\sigma$ is $3$ -fixed-.
Rule 2: And also there is a principle of generating $teta$ that its increment is $0.01$ because of $N$ is $100$ -variable-.
Rule 3: And also sum of $priori$ should be $1$.

My latest try results in $f(x)=exp(-2|x|)/N$.
But for $N = 1$ it violates Rule 3 ! and it is not so close as expected.

Another sample data - for $N = 1$ - is:

teta | priori | Mine
-----+--------+---------------------
 3   | 0.050  | 0.00247875217666636
 2   | 0.100  | 0.01831563888873420
 1   | 0.175  | 0.13533528323661300
 0   | 0.350  | 1.00000000000000000
 -1  | 0.175  | 0.13533528323661300
 -2  | 0.100  | 0.01831563888873420
 -3  | 0.050  | 0.00247875217666636
-----+--------+---------------------
sum  | 1.000  | 1.31225934860403000

Any help appreciated.
Side note, they told me they got these numbers from SPSS software.

Answer 1

Check out Laplace Distribution