i need to calculate correlation significance between two vectors
(x1,x2,x3) and (y1,y2,y3) they are probabilities of two samples to fall in box1,box2 and box3. I need to say are these sample come from 1 distribution or not.

For approximately Gaussian data, the sampling distribution of Pearson's correlation coefficient approximately follows Student's t-distribution with degrees of freedom N − 2. Specifically, if the underlying variables have a bivariate normal distribution, the variable has a Student's t-distribution in the null case (zero correlation).[4] This also holds approximately even if the observed values are non-normal, provided sample sizes are not very small.

My observed values are non-normal, but i have small sample size=3.

How could i calculate the significance or do some test to conclude than my sample are from the same distribution or not?

many thanks