I hope someone can help. I would like to know how to work out the probability of the following:

10 random draws are made. A value is randomly picked from 1,2,3,4 for each draw.

1 is a "sticky" symbol, so if it is picked then that number 1 will stay in place for this draw plus the following 2 draws.

Below are some examples of 10 draws, so each time a 1 is drawn it stays present for the following 2 draws (*=sticky) eg. 1,1*,1*.

4 2 3 1 1* 1* 3 4 2 1

4 1 1* 1* 3 1 1* 1* 3 4

1 1* 1* 1 1* 1* 1 1* 1* 1

The variables are:

Number of draws = 10

Sticky value (The number of extra rounds that the symbol stays in place) = 2

Is there a formula I can use to calculate the average probability of a single draw value being 1? Any help would be greatly appreciated, thanks!