How to determine, calculate and plot a probability distribution for a given set of numbers?
A kernel density estimation based on your data:



Depend on your programming language, you may find the corresponding fitting functions with different distributions.

EDIT

I tried to use the allfitdist function with statistic toolbox in Matlab in your data fitting. 

x = [24.988 25.224 25.212 25.066 25.310 24.963 24.826 24.944 25.490 25.176 24.740 24.988   ...
24.994 24.722 24.510 24.863 25.249 24.931 25.218 24.907 25.459 25.292 25.163 25.447 ...
25.072 25.360 24.976 25.103 25.237 24.845 25.237 25.206 25.109 24.969 24.976 25.194 ...
25.218 24.975 24.777 24.832 24.564 24.637 24.919 24.931 24.944 24.994 25.378 25.042...
25.182 25.151 25.097 25.103 25.030 25.018 24.783 24.722 24.667 24.963    ];

[D PD] = allfitdist(x,'PDF');  


Unfortunately the fitted probability density is not good enough:



The curves for each possible distribution are all overlapped. Like I mentioned yesterday, you may need more sample number to obtain a better estimation.