I stumbled upon two excellent videos by Matt DosSantos DiSorbo. The videos can be found at:
Simple random walk: Hitting probabilities, and
Simple random walk: Expected hitting time
Not sure if he ever transcribed the videos into a text, but if he hasn’t, I have now done it in this paper. To add value to what he did, I also provided some minor maths clarifications to help you follow his videos more easily.
However, a true value-add on my part was to use his example of a simple random walk and provide a solution that applies to stocks and shares movements. If you are interested in finding out what is a probability that your stock value will ever reach a certain level, then read this paper. Furthermore, we have here a simple formula to calculate how long it might take for your stocks and shares to reach a particular value. I also added another interesting trick on how to scale the probabilities to different time horizons. To read the paper, just go here, and if you would like to see the Excel sheet, click here.