There are three boxes, a box containing two gold coins, a box with two silver coins and a box with one of each. After pulling out one gold coin from one of the boxes, that is % chance that the next coin from that same box will be gold

Sounds more like a homework question than a riddle.

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After you pull out the one gold coin from one of your three boxes, what do you have left?

Think of it this way:

|GG| |SS| |GS|

3 boxes, G represents a gold coin and S represents a silver coin.

Your first pick in that box was gold. So, it can only be the first or the second box.

IF you have picked the first box, it would be another gold.
IF you have picked the second box, it would be a silver.

What is the probability that you picked the first box (that is, you will get another gold)?