Is it good Idea for Newbie in Java like me(Python guy) to begine with 3rd Edition of thinking in Java by Bruce Eckel?
The reason is, it is free downloadable. If no any suggestion?

It's a great book. I think 3rd and 4th are not free edition.

I guess you wrong as Planet PDF has 3rd edition on their list and they do not publish illegal content as far I know

Wow! I wasn't aware of planet PDF, nice :)
Thinking in Java is a good book.

Here is a list of sites, from Bruce website, where you can download some of his work

Ok, two have commented that it is great. But is it fit for a newbie?

I think it can be good book when moving from one language to another, so you do not have to go through basics that are fairly similar across languages.
However if you absolute novice to programming world then Head First Java or Java - How to Program would be more suitable as they took from absolute basics

Longtime Pythoneer and now a Small C++er so the issue is, it is fit for me, right?? :D

Yes, you should be reasonably OK with it. The reason why not say absolutely fine is that everyone of us has its own reading style preference.

Cay Hortsman's CoreJava(Eight Edition) and Concepts of Java are also very good books. I like the way he dealt with the concepts.

Longtime Pythoneer and now a Small C++er so the issue is, it is fit for me, right?? :D

Currently I'm jumping into Java (I have a C++ background), and I took Head First Java to get my first Java experience, I haven't finished it yet, but up until now it's a great book.
You might say: how can I learn Java from this book?
But you can trust me, the book will teach you how to program in Java.
The new learning approach they introduce in the book really works, but that's maybe just my opinion.
But the book is maybe a bit too slow for me, as I'm not a programming novice anymore.