Postseason statistics for individual players can be found by clicking the Playoffs tab on tables on their player page. For example, here are the Standard Batting playoff stats for Mookie Betts.

A breakdown of stats in each series that the player has played in can found further down the page in Postseason Batting / Pitching tables. Clicking on a series in the Series table will take you to the overview page for that series. 

Postseason batting, pitching and fielding game logs are also accessible from the menu on the left hand side of the player page. Alternatively, clicking a year in the Season column of the Postseason Batting / Pitching table (or the Playoffs tab of a table like Standard Batting) will take you to those postseason game logs.

On team pages, playoff stats can similarly be found by clicking the Playoffs tabs above the tables.

Links to each series the team played in that year can be found at the very top of the page.

A list of historical postseason series and results can be found here:

And a list of World Series results are on the following page:

Postseason series summaries for an individual season can also be accessed from the relevant league-season page:

On player pages, we note the number of World Series wins for each player at the top right of the player page.

For a World Series win to be tallied for a player in that section, they must have either played in the postseason the year their team won the championship or, if they didn't play, they must have appeared on the World Series roster.

Leaderboards for most appearances on a World Series winner, most games played without appearing in a World Series and most games played without appearing in the postseason are located in the Assorted Leaderboards section of the Leaders & Records page:

Playoff probabilities for each team can be found at the following link:

These are calculated each day throughout the season, and use SRS to estimate each teams chances of winning the World Series, winning the division, making the playoffs etc. There's more information about these calculations here:

This data can be tracked for an individual team for each day of the season on pages like these:

These playoff probabilities have also been calculated for historical major league seasons. For example, here are the daily playoff odds for the 1973 Mets: