Was recently asked this question and I had no idea what it even was asking since it wasn't intuitive. Any help is appreciated.
What is $P(\text{inf}_{t \in [1,2]} W_{t} < 0 | W_{1} > 0, W_{2} > 0)$, where $W_{t}$ is a standard Brownian motion?
To me, this doesn't even make sense since how can we find the probability something is less than 0 given it is greater than zero? Maybe the infimum is in the wrong place, I'm not sure, but this is how it was laid out to me. Of course, once I can understand the question, I can then apply Bayes' rule and continue.