if condition:
    x = true_value
else:
    x = false_value 

There have been endless tedious discussions of syntax on both python-dev and comp.lang.python. A vote was even held that found the majority of voters wanted conditional expressions in some form, but there was no syntax that was preferred by a clear majority. Candidates included C's cond ? true_v : false_v, if cond then true_v else false_v, and 16 other variations.
Guido van Rossum eventually chose a surprising syntax:

x = true_value if condition else false_value

Evaluation is still lazy as in existing Boolean expressions, so the order of evaluation jumps around a bit. The condition expression in the middle is evaluated first, and the true_value expression is evaluated only if the condition was true. Similarly, the false_value expression is only evaluated when the condition is false.

This syntax may seem strange and backwards; why does the condition go in the middle of the expression, and not in the front as in C's c ? x : y? The decision was checked by applying the new syntax to the modules in the standard library and seeing how the resulting code read. In many cases where a conditional expression is used, one value seems to be the 'common case' and one value is an 'exceptional case', used only on rarer occasions when the condition isn't met. The conditional syntax makes this pattern a bit more obvious:

contents = ((doc + '\n') if doc else '')

I read the above statement as meaning ``here contents is usually assigned a value of doc+'\n'; sometimes doc is empty, in which special case an empty string is returned.'' I doubt I will use conditional expressions very often where there isn't a clear common and uncommon case.

There was some discussion of whether the language should require surrounding conditional expressions with parentheses. The decision was made to not require parentheses in the Python language's grammar, but as a matter of style I think you should always use them. Consider these two statements:

# First version -- no parens
level = 1 if logging else 0

# Second version -- with parens
level = (1 if logging else 0)

In the first version, I think a reader's eye might group the statement into 'level = 1', 'if logging', 'else 0', and think that the condition decides whether the assignment to level is performed. The second version reads better, in my opinion, because it makes it clear that the assignment is always performed and the choice is being made between two values.

Another reason for including the brackets: a few odd combinations of list comprehensions and lambdas could look like incorrect conditional expressions.