Conditional Probability for Bernoulli IID

Although 2 dice rolls are independent events intuitively we know that if I have got 6 in the first 3 trials the chance of getting 6 in the next is lower.Also , that is what PROBABILITY means , right ? That if we have huge number of trials number of 6 will be 1/6th.

How is this mathematically explained in statistics i.e. conditional probability of Bernoulli IID given that certain event has occurred in first few trials.