Confusing probability question I have got a task, which seems a quite confusing for me. It is simple: In a market, they sell eggs in egg holders, they store $10$ of them in each. There is $60$% chance, that all of the eggs are ok, $30$% chance, that exactly $1$ of them is broken, and $10$% chance, that exactly $2$ of them are broken(it is random, which one is broken).

We buy an egg holder, and after we grab our first egg, we are sad, because it is broken. What is the probability, that there is one more broken egg in our holder?

The "logical" way would be: $30$% of them have $1$ broken egg, $10$% of them have $2$, so, to have $2$ broken, the chance must be $\frac14$. But I am not really sure if that is the correct approach, since the broken egg can be anywhere, getting a broken one for first may be not that easy, or is that independent?(Maybe, I could use Bayes Theorem somehow)?

Any help appreciated.
I see this as analogous to the pancake problem ... specifically, I would argue that having randomly observed a broken egg, the chances that you are in case C have disproportionately increased.  

Imagine that you had $100$ of your cartons, $60$ of type A, $30$ of type B, and $10$ of type C.  You select one egg randomly from each.  You'll get $3$ broken ones from the Bs and $2$ from the Cs.  Hence your probability is $\frac 25$.
Per the OP.


  What is the probability, that there is one more broken egg in our holder?


thanks to @drhab for the diagram that shows this intuitively :) 

Clarifying Edit

1) What the OP is asking is somewhat equivocal and perhaps this question is better suited to Puzzling Stack Exchange. See points 2) and 3) following.

2) Because it is given that we have a holder with (at least) one broken egg, the proportion of holders without broken eggs is irrelevant to the answer.

3) Because it is given that there can be only a maximum of 2 broken eggs/holder, finding the broken egg in the first slot (or for that matter the 2nd slot,... 9th slot) is irrelevant to the answer. 

4) Given the description in the OP of the holders with broken eggs, two questions may be asked: 


i) What proportion of the egg holders with broken egg(s) have 2 broken eggs? Answer = 25%
ii) What proportion of broken eggs come from holders with 2 broken eggs? Answer = 40%


You'll excuse me if that I took the OP to be asking question i) when others took it to be asking question ii).  ESL and all that... and thanks to @kviiri for pushing me until I understood.