"Extremely low probability events happen all the time" - Does this allow us to draw any conclusions? "Probability of getting any specific hand in poker is the same as getting Royal Flush" - Statements of these kinds seem fairly intuitive to interepret. But recently I thought of the following statement - "There are 10 towns each with its own distinct specialty, like - Food, Landscape, Culture, etc. Now Bob visits exactly one of these towns for his winter vacation."
Now not knowing the fact the bob has no preference whatsoever, I conclude that since he visited town X he must like the town's culture, food, etc. Since the probability of him choosing that specific culture he very less. But this does not make sense as I can say that about any town bob chooses.
Could we or should we draw conclusions like these in a scenario like this? What kind of conclusions we can draw from such an event? What conditions should an event like this satisfy so that meaningful conclusions can be derived?
Thanks in Advance.
 A: All statistics tells you about is correlations -- these two events occur together with greater probability than expected by chance; these two events occur together with lesser probability than expected by chance.
Your specific inference types

Now not knowing the fact the bob has no preference whatsoever, I conclude that since he visited town X he must like the town's culture, food, etc. Since the probability of him choosing that specific culture he very less. But this does not make sense as I can say that about any town bob chooses.

are about causation.  Correlations do not imply causation.  Inferring causation requires more than statistics and probability, one has to go on and do (root) cause analysis and other forms of science.
Statistics helps you find which correlations are explainable by chance, so you do not invest further time/effort in attempting to establish a causal relationship.  Statistics also help you find which correlations are not adequately explained by chance, so you can invest your time/effort investigating apparent causes/relationships.
A: I recommend looking at some philosophy of probability.
There's a basic distinction that many authors make between various kinds of subjective/epistemic/Bayesian probability on one hand, and various sorts of objective probability on the other.  (I'm leaving out some other categories that some authors would add because they are less widely thought to matter.)  This distinction is closely related to the distinction in statistics between frequentist and Bayesian methods.
When we talk about probabilities of card hands, that is usually thought of as a kind of objective probability: there is something about cards and shuffling that makes certain hands come up more or less often.  On the other hand, subjective probability, which might be conceived of as a degree of belief that satisfied axioms of probability, could be applicable, too.  (This would be especially so if you didn't know whether someone might have removed cards from the deck.)
However, your question seems to concern subjective, or epistemic, or Bayesian probability.
I agree with some comments that the issue you raise doesn't seem to have to do with small probabilities.  I also think that when you write "since he visited town X he must like the town's culture, food, etc.", this is a place where one would use Bayes theorem in the context of Bayesian probability.
There is a large, multidimensional universe of math, statistics, and philosophy that is relevant to your question.  You are peeking into a tiny corner of it. I say that not to discourage, but to encourage you to look into it as much as you want.
Here is one starting point for the philosophical side:
https://plato.stanford.edu/entries/probability-interpret/
Introductory textbooks on philosophy of probability include Ian Hacking's An Introduction to Probability and Inductive Logic and Brian Skyrm's Choice and Chance.  Other introductory books include Rowbottom's Probability: Key concepts in philosophy (but there are places where I think the presentation is not great), and Childers' Philosophy and Probability (which is a little more difficult).  An old but useful mathematical survey can be found in Terrence Fine's Theories of Probability.  There are many other books that survey these ideas or focus on particular areas of it.
As my remark above suggests, you might also be interested in literature on the difference between frequentist and Bayesian statistics.  Even the statisticians get philosophical at times, in this area of discussion.  If you're interested in the philosophical dimension, here's a starting point:
https://plato.stanford.edu/entries/statistics/
