Analytical judgment mindset hard to make friends.

Practice makes perfect! Get out of your comfort zone and talk to people. Start slow. Try small talk and such, and listen to what people have to say, and contribute as well. Mainly, just talk to people, lots of different people, and, anywhere, everywhere.

EDIT: I realize that dealing with customers can sometimes feel degrading and upsetting, but… you just have to put up with it. Usually, I find that even though the customer makes me feel like shit, if I just continue to smile and do my job properly, the customer seems to lighten up, as well.

Stop treating people like projects and start treating people like people. If you’re not sure what I mean by this, please let me know.

Think of what your customer must be feeling and try to be sympathetic while you do your best to make the situation right. The customer doesn’t care about the probability factors. He/she just wants the error corrected. In the case you mentioned, you can point out how unusual it is for this to happen, but don’t doubt until you’ve checked all the facts.
Oh, and welcome to Fluther!

Recognising it isn’t the way to behave is the first step. Sounds like you know that so now you just have to catch yourself before you do this again. I think @the_overthinker is right though. Take small steps and work on your social skills. You aren’t alone, there are many people who don’t do ‘small talk’. Do a search for questions about it here. You might be surprised by how many people find this hard.

For some of us, there really is no way around it any more than there is a way to avoid jerking your leg when the doctor taps you on the knee with a hammer. For some of us, social skills are inherently difficult in the same way that the average person cannot figure out the probability distribution of die rolls in their head.

However, even for us, practice will allow you to figure other ways around it. For instance, in your scenario, while the probabilities were that your initial assessment was correct, experience has taught me that sometimes reality is stranger than fiction, and thus any purely quantitative analysis of anything involving human behavior (such as customer interaction) is inherently flawed. The logical conclusion to draw from that statement is that Sherlock Holmes was correct when he told Watson, “Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth.”.

Imagine yourself in the customer’s place. Imagine how you would feel. Believe what they are saying until proven otherwise.

You may calculate the odds of something happening, but do not assign a situation to the odds without checking it out first.