This really does not change anything.
Yes the system might be designed so that the second legendary has a lower chance than your first. But it is the same for EVERYONE. Hence the RNG is affecting everyone the same way. There is no person being affected differently than anyone else.
What the actual drop rate for the second legendary is, doesn't change the fact that your pool of available drops has now gone from 7 to 6. Making the chance of getting the one you want larger, WHEN YOU GET A LEGENDARY.
Without a legendary you have 1/7 chance of getting the legendary you want. What the actual drop chance is, is irrelevant to this.
When you have your first legendary(the wrong one), you now have 1/6 a chance to get the legendary you want. Again the actual drop chance is irrelevant to this.
The probability for getting the exact legendary you want is independant from the probability of getting a legendary.
The actual drop rate of each legendary doesn't mean much. The system as analysed by the thread of drop rates, show that the amount of content you need to do for each legendary is increasing for each legendary you get.
BUT this does not take into account that you are suppose to be progressing your character, becomming stronger and doing harder content (and easier content faster, making you able to clear more in the same time as you did before your first legendary)
Harder content gives you more "kill points".
The amount of time from your first legendary to your second and your fourth to fifth is roughly the same. If you got your first legendary after a month, then you would get your second after another month, and your third after another month again. Of course there is still the element of RNG below it all, so that some might not get it as soon as they should or some get it earlier.
EDIT:
Even if they use a fixed drop chance for each legendary, the above is still true.(personally i think they fixed each one).
That is for each legendary you already have, the chance for getting the one you want from the remaining legendaries is increasing.
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You can not get the same legendary twice..