"the likelihood that the twenty-first century will not be much like the twentieth" ---> this means that because of what happened in the twentieth century, the writer expects that the 21st century will also have a lot of political change. And therefore it will not be the same the 20th century.
If we break it down the writer - I'm guessing historian? says:
-They studied past history
-There was a lot of political change in the 20th century
-They expect that there will be political change in the 21st century.
-They are almost 100% sure that it will change -- (the inevitability) --- if something is inevitable, it means that it will happen