The bridge isn't 60% "real." It has a 60% chance to work (or not work, as it were) on non-believers. Allow me to explain...
Those who pass their save and become non-believers in the shadow conjuration...
A creature that succeeds on its save sees the shadow conjurations as
transparent images superimposed on vague, shadowy forms.
...must make a percentile roll to see if they can use the bridge (after passing the Will save). If they fail their roll (40% chance) the effect created (in this case, a shadow version of wall of stone) does not apply to them for that usage, and they cannot use the bridge. If they pass the roll, they can cross safely.
Shadow Conjuration
...
Shadow objects or substances have normal effects except against those
who disbelieve them. Against disbelievers, they are 20% likely to
work...
Shadow Conjuration, Greater
This spell functions like shadow conjuration, except that it duplicates any sorcerer or wizard conjuration (summoning) or conjuration (creation) spell of 6th level or lower...
...and nondamaging effects are 60% likely to work against nonbelievers.
This roll must be made each time the effect is "applied" (in this case each time a non-believer attempts to use the bridge) because of the non-believer's uncertainty of success, which comes from the fact that they see the shadow for what it is.
Note that anyone can intentionally fail their Will save (thus avoiding the percentile roll) in order to use the bridge safely. On a similar note, objects always pass their Will saves per the spell description, so will always have a 60% chance of passing. However, I might houserule it in such a way that an object will always pass its Will save and will always fall through, in the interest of making sense.