Rules and Errata

It would seem to follow RAW to me.
"When you explore, draw the top 3 or # cards of this location. Keep 1 and return the rest in any order, then do 1:"

RAW, in the Counting Resources sidebar says:
"If you’re required to do something with a certain number of things and there aren’t that many things available, use as many as there are...
Note that this only applies when you are required to do something. If you have the opportunity to do something that requires a limited resource, and you don’t have enough of that resource, you cannot do that thing."

So the question is, what is required and what is optional? If the explore is optional, but once the character has chosen to explore the location power is not optional, then you would have to draw 0 (instead of 3 or #) card, keep 1 of nothing, return the rest of nothing, then do 1 of the options. If the act of exploring is ignored and the location power is seen as being optional, then you can't explore if there is less than 3 or # cards at the Base (even if there are still 2 cards at Tier 3+!).