To follow up on Quid's comment, the share classes themselves will define what level of dividends are expected. Note that the terms 'common shares' and 'preferred shares' are generally understood terms, but are not as precise as you might believe.
There are dozens/hundreds of different characteristics that could be written into share classes in the company's articles of incorporation [as long as those characteristics are legal in corporate law in the company's jurisdiction]. So in answering your question there's a bit of an assumption that things are working 'as usual'. Note that private companies often have odd quirks to their share classes, things like weird small classes of shares that have most of the voting rights, or shares with 'shotgun buyback clauses'. As long as they are legal clauses, they can be used to help control how the business is run between various shareholders with competing interests. Things like parents anticipating future family infighting and trying to prevent familial struggle. You are unlikely to see such weird quirks in public companies, where the company will have additional regulatory requirements and where the public won't want any shock at unexpected share clauses.
In your case, you suggested having a non-cumulative preferred share [with no voting rights, but that doesn't impact dividend payment]:
There are two salient points left related to payout that the articles of incorporation will need to define for the share classes:
(1) What is the redemption value for the shares? [This is usually equal to the cost of subscribing for the shares in the first place; it represents how much the business will need to pay the shareholder in the event of redemption / recall]
(2) What is the stated dividend amount? This is usually defined at a rate that's at or a little above a reasonable interest rate at the time the shares are created, but defined as $ / share. For example, the shares could have $1 / share dividend payment, where the shares originally cost $50 each to subscribe [this would reflect a rate of payment of about 2%].
Typically by corporate law, dividends must be paid to preferred shares, to the extent required based on the characteristics of the share class [some preferred shares may not have any required dividends at all], before any dividends can be paid to common shares. So if $10k in dividends is to be paid, and total preferred shares require $15k of non-cumulative dividends each year, then $0 will be paid to the common shares. The following year, $15k of dividends will once again need to be paid to the preferred shares, before any can be paid to the common shares.