It doesn't matter what it seems. Simply asserting something doesn't make it true, you need to demonstrate it before you can make sweeping assertions based off that ignorance.

I think I basically did make a solid probabilistic argument.

This is what I think you're stating we should believe. If we assume this segment is a constant, we can just say that the probability that at any given point in time is also a period of time with consciousness is basically zero. With that, I am making the argument that since the probability that consciousness should exist at any given time (including this current time) is basically zero, then we should assume that it has existed in the past.

Argument from ignorance. There's no way for you to know that, let assume the probability based off it.

I actually think other people have written far more on this topic than myself, with much more thought put into it. That's also why there's really interesting topics such as Boltzmann brains. It isn't an argument from ignorance, but you can keep screaming that if it makes you feel better, I guess it doesn't really matter.

That says nothing about what came before or what comes after. In what way is that demonstrative of the continuation of consciousness?

There's also a lot more written on this philosophically, which is why I was able to link to the philosophical topic in my first comment. You're the one arguing that your magic unique consciousness ID can only be invoked once.