A problem is difficult when its potential consequences are serious and the best option is not obvious. But the best option can be non-obvious for two very different reasons: either it requires a lot of information and thus a lot of work to gather that information (like choosing a medical treatment), or it depends on randomness or other variables outside your control and understanding (like choose your lottery numbers, assuming someone gives you a lottery ticket).
For the latter case, it's pretty clear that you can choose randomly and shouldn't worry about your decision. For the former case, it's reasonable to "worry" in the sense that you should feel an urgency to gather the required information efficiently. Of course, it's not really that simple, because you have to optimize the cost of gathering information against the potential cost or gain from the decision itself. Also, the two reasons from the last paragraph are more like a continuum, because "randomness" is often effective randomness, i.e. you can't feasibly predict the outcomes despite them being deterministic.
"Clarity" is dependent on what level of information you already have and what analysis you've already done.
In some circumstances, you've already done whatever investigation, research, and thinking can reasonably be done. If the choice is still hard, then the choice is likely to be of similar value either way and you may as well choose arbitrarily.
But in other circumstances, there's still investigation, research, or thinking that can be done (at a level of effort which is reasonable based on the importance of the decision.) In that case, one choice or the other may become clearly better if you are patient and diligent in the decision-making process. So be as patient as the decision warrants.