Hi Ruhm,
Happy to help. So most applications will have an 'optional essay' and/or a place to address additional info or discuss this type of past challenging situation. If at all possible I would use THAT space to address this, as opposed to your main personal statement which is usually more about the present and future-- i.e. why you are seeking this degree; what you plan to do with it; what you bring to the program etc.
Of course you cannot change the past but discussing it in a mature way; keeping it concise and showing how you came back from that and what you've learned from it is the best way to deal with it. The more you've shown positive academic accomplishments since then, the better. Your test scores will also help mitigate prior academic failures, to a certain degree. That said you will need to explain what happened and again, why that will not happen again.

And of course I don't know exactly what each academic situation was.
Hope that helps, feel free to follow up and good luck!