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Probability theory is a branch of mathematics that deals with the likelihood of events occurring. It is the foundation for many disciplines including statistics, economics, and engineering. The essence of probability theory lies in quantifying uncertainty and making calculated predictions based on available data.

In the context of our exercise, probability theory helps us determine the chance of picking a ball of a certain color from a box when the balls are selected with replacement. To calculate this, you would use the formula:
\[\begin{equation} P(X) = \frac{\text{number of favorable outcomes}}{\text{total number of possible outcomes}}\end{equation}\]

Each time a ball is selected, it is considered an independent event because being picked once does not affect its chances of being picked again due to the replacement. This is a key concept in probability theory called independence, where the outcome of one event does not influence the outcome of another.

Combinatorics is a field of mathematics primarily concerned with counting, both as a means and an end in obtaining results, and certain properties of finite structures. It includes a variety of topics, such as graph theory, enumeration, and design theory. One of its core principles is determining the number of ways specific outcomes can be achieved, which is fundamental in calculating probabilities.

Within our particular scenario, combinatorics comes into play when we identify the different sequences in which balls can be drawn from the box. For example, if the sequence we're considering is drawing a red ball followed by a green ball and then a blue ball, combinatorics helps to understand this specific arrangement. This is where the concept of permutations and combinations would typically come into play. However, when the balls are selected with replacement, the combinatorial calculations are simplified as each draw is independent and the total number of possibilities remains constant.

Conditional probability is a measure of the likelihood of an event occurring given that another event has already occurred. This concept is integral to understanding more complex probability scenarios where events are interdependent. The probability of event A given event B is notated as P(A|B).

In the exercise scenario, although we deal with replacement—meaning each event is independent from each other and hence does not fit the exact definition of conditional probability—it’s crucial to understand this concept to grasp more complicated probability problems where replacement is not involved. For instance, if the balls were not replaced, the probability of drawing a ball of color B after having already drawn a ball of color A would depend on the prior outcome and thus be a conditional probability. The computation involves adjusting the probability of B based on the occurrence of A. However, since our exercise is with replacement, each draw is independent, and the conditional probability in standard form is not required.