Let's solve the problem step by step.

1. Sample Space: The sample space includes all the possible outcomes when one ball is randomly picked from the bag. Since the balls are labeled $A, B, C, D, E, F, G, H$, the sample space is: $S = \{ A, B, C, D, E, F, G, H \}$

2. Event of Choosing a Letter from $A$ to $D$: This event includes all outcomes where the ball picked is labeled with a letter from $A$ to $D$. So, the event is: $E = \{ A, B, C, D \}$

Would you like further details on any part of this solution?

Here are five related questions you might find useful:

1. What is the probability of picking a ball labeled $A$?
2. How many total outcomes are in the sample space?
3. What is the probability of the event $E$ occurring?
4. If one more ball labeled $I$ is added, what will be the new sample space?
5. How does the probability of event $E$ change if there are now ten balls?

Tip: The sum of the probabilities of all outcomes in a sample space is always equal to 1.