First, I'll try to give you the intuition of why it doesn't work like that:

Imagine you have one regular die 1-2-3-4-5-6, and another die with colours instead Blue-Red-Yellow-Green-Orange-Pink.

You roll the first die and obtain 6, that was a 16%.

You then roll the second die. What would that mean to "have a smaller chance to roll a 6 again"? Which colour is "6"? Is that Pink because it was the last of my list? That's completely arbitrary. It doesn't make sense that my first roll with change the probability of obtaining a colour or another, so there is also a 16% chance of obtaining each colour.

Now, if I write some numbers on top of the colours, does that magically change the probability of obtaining the "Pink 6" just because I obtained a 6 before? Surely not.

And if instead I rolled the first die a second time, why would that be any different? It's not like objects have some "magical memory" that remember how often it rolled 6.

Now, here is why you did think it worked like that in the first place:

If you roll the first die, don't look at its result, then roll the second die, then yes, the probability of getting two 6s is quite low: 1/36 = 3%

Similarly, if you roll the first die, don't look at its result, then roll the second die, and then I look at both and say 'I promise you that there is at least one 6', then the probability of a double 6 remains quite low: 1/11 = 9%. What's the difference? Well, I didn't tell you whether the first or the second was a 6, so you have less information than in your example (where you knew that it was the first who was a 6). Just a slight change in information and the probability is different.

And lastly, in nature, there is a lot of things that look random but aren't. For example, there is a 50/50 chance of being night or day, but after enough night the day eventually come, because that's not actually random in the same way a die works.

But in the situation you described:

• You have total knowledge about the first roll. It's a 100% chance of obtaining a 6 because you know the 6 happened. That's a fact that cannot be changed.
• You have zero knowledge about the second roll. It's a 16% chance of obtaining a 6 because the roll is fair and nothing is influencing it.