I have a list of categories A, B, C, etc, each with a probability:

A   .015
B   .005
C   .02
D    ... etc. 

I need to find if the difference between two of these categories, say

diff(C,A) = .02 - .015 = 0.005

is statistically significant. I have been using a Standard Error of Differences with the probabilities but since I don't have a normal distribution (and obviously not even continuous), what test would be recommended?

Edit:

The source of the data is essentially a list of the categories, these are not experiments I am performing but data that is given to me. The size of the list can vary but let's assume it's reasonable small (under 500).

I have a list of categories A, B, C, etc, each with a probability:

A   .015
B   .005
C   .02
D    ... etc. 

I need to find if the difference between two of these categories, say

diff(C,A) = .02 - .015 = 0.005

is statistically significant. I have been using a Standard Error of Differences with the probabilities but since I don't have a normal distribution (and obviously not even continuous), what test would be recommended?

Edit:

The source of the data is essentially a list of the categories, these are not experiments I am performing but data that is given to me. The size of the list can vary but let's assume it's reasonable small (under 500).

UPDATE:

Accepted the answer below but you should read the comments attached to the answer for full understanding of the resolution.

I have a list of categories A, B, C, etc, each with a probability:

A   .015
B   .005
C   .02
D    ... etc. 

I need to find if the difference between two of these categories, say

diff(C,A) = .02 - .015 = 0.005

is statistically significant. Since I don't have a normal distribution (and obviously not even continuous), what test would be recommended?

I have a list of categories A, B, C, etc, each with a probability:

A   .015
B   .005
C   .02
D    ... etc. 

I need to find if the difference between two of these categories, say

diff(C,A) = .02 - .015 = 0.005

is statistically significant. I have been using a Standard Error of Differences with the probabilities but since I don't have a normal distribution (and obviously not even continuous), what test would be recommended?

Edit:

The source of the data is essentially a list of the categories, these are not experiments I am performing but data that is given to me. The size of the list can vary but let's assume it's reasonable small (under 500).