Calculating the Probability of Consecutive Events in a fixed Population

Question

I want to find an equation that will calculate the probability of 3 events occurring in a row (consecutive) given a population.

Example

1. I have 5 empty slots in a row to place balls __ __ __ __ __
2. Balls are drawn randomly from a bag (80% chance of black, 20% chance of white, each draw is an independent event that does not affect the next draw)

3. 1 possible arrangement after all the balls are drawn is B, W, W, B, W

4. What is the probability that after all the empty slots are filled, I will have AT LEAST 3 black balls in-a-row? Example would be W, B, B, B, B

Equation Inputs:

1. Sample/population size = X
2. Probability of drawing back ball = P(B) [which then means P(W) = 1-P(B)]

Equation Output:

Probability of having AT LEAST 3 black balls in a row anywhere in the population

Note

Of course with a small population, I can simply brute force each scenario and sum the probabilities, but the reason I need an equation is because my population size could be 1000