This page of Wikipedia about confidence interval says:
The confidence interval can be expressed in terms of a single sample: "There is a 90% probability that the calculated confidence interval from some future experiment encompasses the true value of the population parameter." Note this is a probability statement about the confidence interval, not the population parameter. This considers the probability associated with a confidence interval from a pre-experiment point of view, in the same context in which arguments for the random allocation of treatments to study items are made. Here the experimenter sets out the way in which they intend to calculate a confidence interval and to know, before they do the actual experiment, that the interval they will end up calculating has a particular chance of covering the true but unknown value. This is very similar to the "repeated sample" interpretation above, except that it avoids relying on considering hypothetical repeats of a sampling procedure that may not be repeatable in any meaningful sense. See Neyman construction.
Suppose I have a 90% confidence interval for the weight of a population to be [100, 110]. So, how can I express it according the above interpretation?
It says about confidence interval from future experiments as if it completely ignores what I have already obtained, so how it covers the calculated interval.
I think I understood it and just need confirmation: Because we have already obtained [100, 110] interval, this interval is fixed and no more a random variable, so we can say, we are 90% confident that this interval includes true mean.
However, if we regard confidence interval as a random variable, we can say there is a probability of 90% that 90% confidence intervals calculated this way include true mean...